I would let them rest. Zyrxog is a formidable opponent, and it's worth allowing your party to recuperate. I wish that mine had (see my latest entries in the obit thread). Since the drow are "thralls", they have presumably been subjugated by the stone brain. This means that they have dominate person in effect.
My interpretation is a little loose, but it seems to me that the stone brain is really just an extension of Zyrxog. When a person is dominated by it, the control is transferred to Z. Given that assumption, Z receives sensory impressions from all of his thralls. Therefore he will be quite aware of their deaths.
However. Zyrxog is extremely self-confident and IMO entirely willing to allow the PCs to come to him since it is plain that this is what they intend. True, they just killed a few of his thralls, but there is a near infinite supply of drow in the Underdark. He just needs to go to the store to pick up a few more. No biggee. In this case, I think that this is an ok foe to just sit and wait for the PCs to come to him. I hate to do that for a lot of dungeons, but it made sense for Zyrxog (in my head anyway).
So let 'em rest. You've got a good chance of killing a PC as it is. If you bring the fight to them, you've got a great chance of killing them all.
Usually I agree with Eltanin, but come on, would you be comfy camping in the room where Zyrxog has been storing dead bodies? And what did the party do with the prisoners? I think the business of not giving up ground taken gets taken to a bit of an extreme. If Zyrxog can muster up any more thralls who are presently outside his lair, then they are likely to visit in the middle of the night and create an inconvenient scene, disturbing the party's rest and making it difficult for spellcasters to be at full capacity in the morning for the showdown with the Big Z. If he can't muster any more followers just now, then if he moves minions out from the inner lair during the night while the party is sleeping at the inn, all he's doing is spreading his existing defenses thinner, and the party will be fighting them on terrain that is already familiar.
At the least, if the party hasn't taken out the octopins in front of the door and the naga, those two should visit during the night. If you're gonna camp, you've at least got to make sure your immediate environs are clear. But personally, I'd have the Big Z pay a visit in the middle of the night. A nice, tasty midnight snack of brains! Ohhhh yes. Have Zyrxog go until he either gets his midnight snack or takes damage, then make his getaway, plane shifting to the ethereal if necessary.
Camping in the dungeon should be situational, not an automatic response to being a little worn down. There are many times when it's appropriate to retreat to a safe spot and rest; there are occasional times when the situation dictates underground camping. Since it's a hop skip and a jump back to the surface here, the party should (a) ensure the outer lair is completely clear of enemies, and (b) retreat to rest if they don't feel ready to take on Zyrxog.
My party rested once inside Whispering Cairn, because 3 of the 4 were unconscious but stable after the battle with the wind warriors. They rested two nights inside the Temple of Hextor in TFOE--the adventure was designed this way, since it was not easy to sneak in and out at will, for my party at least. They rested inside the Twisted Branch lair, but they had already killed the chief and reached a bargain with Hishka, so they were guests. I just don't think it's that situationally appropriate in either of the dungeons in HOHR to sleep in the dungeon rather than at the inn where they are relatively safe--since it's easy enough to get in and out of the dungeons. If they do retreat to rest, reward them by spreading out Zyrxog's defenses a bit more--maybe have him put one of the octopins from his sanctum in ambush where the drow sentries were. Have him scry on this octopin so he knows the PCs are coming, but since there'll only be one octopin in the final encounter, that will be a bit more manageable for the PCs. (As written, the Zyrxog encounter is one of the toughest in the AP, for sure).
It's actually not all that hard to make it straight through to Zyrxog with plenty of fight left. If the PCs haven't burned too many resources on the drow, anyhow. If the PCs are smart and have done their divination homework, they can easily bypass the stone brain (protection from evil), the advanced octopin, and the vrock. So they should have plenty left for Zyrxog at the end. As long as they have the right spells handy (spell immunity vs. mind blast is ideal, fly or a barrage of rapid shot arrows is very handy, as is summoning a flying ally, and of course resist energy). If they haven't done their homework by contacting their friendly local deity, they are in for a rough ride whether they're at full strength or not.
Ok, I take Peruhain's points. Especially since the city is in fact just a hop skip and a jump away. I'm definitely feeling gun-shy about killing everyone though, since I only narrowly averted a TPK with Zyrxog just last week.
I still think that my points about Zyrxog are reasonably valid. The naga though, I'd forgotten about the naga. He should definitely make an appearance. Nothing like a good ol' fireball first, charm person afterwards. (I'm not actually advocating that tactic, it's just funny to think about).
In another rebuttal of Peruhain's points, the stone brain is NOT easy to protect against. Protection from evil and magic circle against evil (both in use in my group) prevent immediate dominating. However, since dominate person lasts for DAYS, as soon as the party's buffs wear off, they are in a bit of situation. So is the DM. In fact, I'm in that situation now, and I'm going to go off and start a new thread about it. So there.