We picked up right where we'd left off, with the PCs finishing their second short rest in the goblin cave, after having rescued Lord Sindar from the goblin sub-boss Yeemik and his cronies. Although everyone had full hit points, the spellcasters were almost out of spells, so the group was cautious. They sent the Tylow (the halfling rogue) ahead to scout, but since he couldn't see in the dark, he didn't want to risk too much light when they got to an open area where he knew goblins were present. So instead they asked Elsa (the half-elf barbarian genki girl) to scout into the room.
Good idea in theory– not so great in practice, as Elsa rolled a 1 on her stealth check and accidentally scraped her "butter knife" (as Gimlet has taken to calling Elsa's greatsword) against a stalagmite, alerting the goblins to her presence. One player surge later, and three more slaughtered goblins, including one who was running to tell the boss. Once that was done, they explored the room, to find a peculiar arrangement of dammed-up, easy-to-knock-away pools. Boggling over this for a bit, they finally came to the consensus that this was a defensive "trap" of sorts– anyone following the main stream up the central cave could have gallons of water and debris dumped on them on short notice. (They didn't know this, but that is in fact exactly what the goblin scout on the bridge they had killed in the previous session was sneaking off to tell them to do. Fortunately for them, Mei took him out with a single shot, so the PCs didn't get to experience being washed away.)
From there, there was basically one room of the cave left: Klarg the Crusher (a bugbear), and his minions, an enormous wolf and a pair of goblin mooks. I had warned the players OOC that play reports online had identified this as a tough encounter for a 1st level party, and so they were cautious, opting to spy on Klarg rather than go charging in.
Based on how 5E is playing so far, I think that they might have been able to fight it out, especially with Lord Sildar's assist, but it really would have been up to the dice, and historically dice have tended not to be kind to us. So, as was becoming their S.O.P., they sent the rogue in to scout it out. With some very good stealth rolls, he came to the conclusion that Brannar Diamondheart was not in Klarg's room. He also spotted a treasure chest, which did tickle the group's greed, but not enough to overcome their desire not to have a fight that wouldn't necessarily get them any closer to rescuing their patron.
And so, they left the goblin caves, recovered their horses and wagon (which had fortunately not had any random encounters), and went on to town. There they delivered Brannar's supply wagon and collected their fee, avoided a pair of Redcloak toughs wandering the streets, and checked into their rooms at the Stonehill Inn. They determined by chatting with the various townies that Brannar had never showed, so that left them temporarily stymied. They resolved to return to the goblin cave the next day and find some goblins to interrogate, and went to sleep, magically waking up at 2nd level the next day! ;)
Again, their plan was good in theory, but when they got to the cave, they found that the goblins had evacuated. They did find a crumpled note, however:
Return to Cragmaw Castle. You are all but useless. Fortunately you delivered the dwarf, so you may live.
Unless King Grol decides otherwise, of course.
None of them had ever heard of "Cragmaw Castle," including Mei, whose family had lived in this area for generations. (She rolled a 20 on her Int check to see if she could think of where it might be, and still came up with nothing.) They decided there was nothing for it but to go find some goblins. Hexcrawling time!
The hexcrawl aspect of the game was something that I added; the module as written had a basic regional map and an encounter table, which I replaced with a hex map with more varied encounters by terrain type. The characters decided to strike out for the ruined town of Pelann, as it was where Mei's family was originally from, and they had no real plan otherwise. There was some concern about rumors that a dragon had recently made its lair in the town tower, but the general consensus seemed to be, "So we just won't go to the tower."
The random encounter tables didn't feel cooperative: the day turned from sunny to cloudy, but otherwise nothing of note happened until they reached Pelann. When they got there, they were confronted by a makeshift sign set in the middle of the road that read "DANGER! Plant monsters AND zombies! Turn back now!" However, the town seemed completely quiet and deserted, so they pressed ahead. 
The first building that caught their eye was the remains of a tavern called The Brown Horse. Peeking in the windows, they saw the ash-coated bodies of the people who had died in the tavern when the poisonous ash cloud from the eruption of Mt. Thunderdelve descended on the town with almost no warning. Given that the eruption was fifty years ago, they were a little perturbed that the bodies had remained undisturbed by looters or scavengers, but they also remembered that local folklore is that "the dead are unquiet," so probably no-one had wanted to risk it.
Gimlet, on the other hand, decided it was no good letting zombies just lay around, so he blasted one of the bodies with a holy spell. Of course, several zombies rose up and attacked; fortunately the party was able to handle them without too much difficulty. They then decided that this wasn't getting them any further on their goblin hunt, so they left Pelann behind and struck out across country again, but Mei was at least content to have seen her ancestral home for the first time.
Again the encounter tables had little to say; after having spent most of the day wandering they decided to take a more active approach and deliberately search for signs of goblins. With a few Survival checks, they eventually found some recent boot prints and followed them, catching up with a small hobgoblin war-band just as it was getting dark. Charge!!!
They quickly dispatched two of the hobgoblins and captured the third, Tylow managing to land a critical hit with a sneak attack (4d6+3, ouch). Elsa, as the only member of the party who could speak goblin, attempted intimidation, but the hobgoblin's martial discipline gave him the resolve to be defiant. Morgo the Magics Master decided to take a different approach. "Think you're tough, eh? Let's see how tough you are being mercilessly tickled by a mage hand spell!"
This was something the hobgoblin had not anticipated. ;) And me neither! I finally decided this would be Morgo's Charisma check vs. the hobgoblin's Wisdom save as a willpower check (although upon reflection, Con might have been more appropriate). Either way, Morgo's roll blew the hobgoblin's out of the water, and the hobgoblin gave in.
He told the players the rough location Cragmaw Castle (at the southern tip of the mountains, near Old King's Nest), and that it was ruled by King Grol, who was mighty and powerful and leader of all the Cragmaw goblins. When asked about "the spider" who had signed the note to Klarg, the hobgoblin told them that Spider was someone who paid King Grol to do things for him up on the surface, because the Spider preferred to stay underground. He also told them that there had been orders to recover the dwarf Brannar Diamondheart, but more importantly, the dwarf's maps, but that was all the hobgoblin knew, because his war band had been away from the castle for several days and was actually on the way back when the PCs captured him.
They left the hobgoblin tied to a tree and went off to camp for the night. The next morning, they made for Cragmaw Castle, passing through the quiet ruined village of Coneyburr. The only encounter of note during the day was they spotted a squad of soldiery camped in the plains southeast of Coneyburr, but so far in the distance they couldn't make out any of the banners and so had no idea who it was (but didn't feel like investigating, either). Near the end of the day, they finally make it up the mountains and found Cragmaw Castle.
The reason nobody had heard of it, it turned out, is that it was a ruin from the days of the North Kingdom, nestled in a small valley and thus not easily spotted unless you already knew where to look. It looked like it had once consisted of several tall spires, but over the centuries earthquakes and the simple decay of time had caused it to mostly collapse on itself, leaving little more than one viable level aboveground. (What might be in dungeons underneath, who knows?) The party found a fairly hidden place to camp for the night and observe, looking for patrols and other activity, and that's where the session ended.
Impressions? So far I'm very pleased with 5E. As I posted on the ENWorld boards: "When I actually broke down and started playing around with 5E, I felt a profound wave of relief. I am so burnt out on the 3.x engine, and the past couple of years of Pathfinder have not helped. I've been using Hero Labs, and even with that the piles and piles of options, traits, class archetypes, and ALL the modifiers... I can't take it any more. I eventually tried to get my group to switch to Savage Worlds, just to get away from it."
I also wonder if the stories I've heard of PC fragility have not been overstated. Not that I particularly want to see PCs dropping left and right, but much of what I've read online made it sound like low-level characters were barely able to cope with even the most trivial encounters. So far the PCs have mostly gone through the opposition like a hot knife through soft butter. I'm actually fine with this, as it makes me feel more confident I can throw whatever I feel like at them, especially now that they've got enough hit points that they're not likely to get one-punched.
As the game continues, I know I'm going to be drifting further away from the adventure as written and more into "my campaign," but I'm really impressed with how good of a jumpstart the Starter Set provides. I'd say it's easily as good for the modern gamer as Keep On the Borderlands was for gamers in 1979.
Dungeons & Dragons is back, baby. :) Gygax and Arneson be praised! ;)
 Of course Pelann was the one major encounter area I had not prepped– but I had the notes from the module, and after a bit of furious scrambling to print out a map for the players and quickly re-reading a few paragraphs in the book, had enough to roll with. But next time they decide to go there, I'll be ready. ;)