My party has haphazardly gone right through the middle of the dungeon and while this produced a few fights that were a lot harder than intended they pulled it off and finished of the boss of the campaign, and recovered the macguffin and it was really late so we ended the session.

Now we'll pick back up, and they'll find a way to do a long rest and want to explore the rest of the dungeon. It is populated with quite a bit of content they bypassed including a puzzle that could be fun but seems quite anticlimactic as they already cleared out the "hard' fights.

Would you just let them explore it normally? had wave most of it to rush to the epilogue? just go straight to epilogue and options for the next campaign?

I guess I can just ask the players, but if they would enjoy the exploration being told "you've done the cool stuff' will probably suck the life out of the remaining stuff.

I have some players that actually do enjoy checking out the rest of the dungeon/lair/hideout after the boss fight, just to see what's there.  In a way, it's sort of a "victory lap" for the party, as they find out what other interesting loot, magic trinkets, and bits of lore they can pick up.  If you've got a little time to prepare, it might be worth a try.

You could add in some things like: bits of backstory on the boss or vague references to how they got their power, minor magic items that are more stylish or interesting than useful, a reference to a dangerous beast lurking in unexplored territory, or a treasure map in a far-away location.  You could drop some plot hooks for the next adventure, in the areas they haven't explored yet (the villain's private library is my favorite place for this).  And if there are intelligent minions still in the dungeon, then the death of the boss can totally change the dynamic of remaining encounters- the minions may be competing for dominance, or just trying to loot the place themselves, for example.  

So yeah, there's stuff you can still do with that, but it depends on what your players are interested in, and how anxious they are to get to the next story.

Well, it depends on your players.

I as a player, prefer unmapped areas to remain un-mapped. Mostly just like having the options or realism of stuff, especially if the dungeon is still filled with puzzles or enemies that could kill you.

For example, in one campaing we stumbled into a grand ritual area in a dungeon with many enemies, the cult Boss lady and the main mcguffin (a kidnapped person), and after a hard fight (this was at level 2), we finished up everyone but still had many rooms that were undiscovered.

- We could have just grabbed the body of the boss lady, the kiddapped person and find the entrance to deliver her (another NPC was blamed for the dissapearance). And that was it.
- But, since we decided to investigate the rest of the rooms (and fight throught some traps and monsters still around), we found very important information about what was happening and more evidence that blamed some nobles that were in league with the cult. That made the next part of the adventure more interesting. (off course in this case it was the beginning of the campaing, not the posible ending). After we cleared everything, the DM did say: "there's nothing more here for you to find, just some random rooms with trinkets and stuff. do you want to grab something? (rolls on trinkets table)" "after some time, you find and exit and go back to the city and blah, blah, blah, blah...."

So as my advice, leave the dungeon as is (considering the possible changes of the situation at hand), and ask your players at the beginning what they want to do next. Leave and claim glory, or investigate and find moar treasure/hints, etc...
- For example, an enemy that lives after the attack could escape somewhere else and continue the work of his boss, becoming the new big bad. Or maybe when they investigate around, they found some clues about some other research the Boss was doing and that leads to the next adventure (if you dont have any idea, maybe just a cryptic or encrypted message that they need to investigate somewhere else).

Hope this helps

It would be pretty easy to say the rest of the enemies fled after the boss was killed, in fact, that’s probably what makes the most sense. Even the dumbest minion will realize they don’t have a chance against the people who beat the boss. 
For a bit of fun, you can always have one of the survivors be the boss of the next campaign, putting to use lessons they learned from this boss’ defeat. 
And you can always save the puzzle for another dungeon. Good prep work is never wasted, just sometimes you did it a bit earlier than you needed to.

If you’re asking about personally, I agree it might feel anticlimactic. The really crappy part would be finding, like, a vorpal sword or other cool loot but never getting to actually use it.

I’d just narrate the party getting back to town and calling it good. Though I do like a nice wrap-up. Tell the players what happened to any NPCs they liked. And let the players describe what their characters do now that they’ve saved the world. 

If you get to the next session and the players say essentially "ok let's blow this pop stand", then I would just recycle elements of the dungeon they never explored for later use. 

If you  have a continuation planned for these characters then I would run the rest of the dungeon and let them explore it before moving on to the next thing.

However, your comments seem to indicate that this is the end of the campaign. Are the characters retiring? Not being played anymore? Do the players KNOW that the end is coming?

If you are ending things then it really isn't worth taking the time to explore the rest of the dungeon that won't mean much for these characters since they won't be played further. In this case I would go with Charles suggestion and recycle the content into a future dungeon and save yourself some work. Just shift to the epilogue.

The only problem with going to the epilogue is that it will be a real let down for the players if they weren't expecting the campaign to end. The players expect to play characters that they are attached to and one of the biggest shocks a DM can deliver is to say "Well. Campaign is done now. Won't need those characters anymore. What do you want to play next?", especially if the DM hasn't let the players know in advance that the campaign is ending.

If they decide just to leave then let them, and keep all the bits they didn't find for another dungeon later :)

I would let the players decide. What you as the dm need to do is decide how the creatures in the dungeon react to the bosses death. 

What kinda dungeon is it? Would the minions show up latter looking for the boss, maybe interrupting the players long rest. Maybe now the bosses is dead all the minions leave or maybe they attack the players in force, making for a "run for your life" kinda adventure? 

Any time spent in a BBEG dungeon after killing the villain should be spent exploring. This could mean uncovering pieces of backstory (to add a little more to the why section of the plot), plot hooks for the next adventure, magic charms, or treasure. However, the challenges of the game should be over. A couple rolls is fine, but combat encounters, as well as puzzles and traps, are best avoided because they will feel pointless to your players.

Luckily for you, avoiding combat encounters should be easy. Any monsters in the dungeon the PCs would have fought were probably working for the BBEG. After the BBEG dies, they will probably surrender, as any further fighting is a lost cause. Instead, these interactions open up a window for some interesting social scenes.