Your dwarves are doing nothing because you've given them nothing to do. If you've given them nothing to do you don't have to worry about what they'e doing, just expand your tavern, give them nice things to look at until you think of something to do.
Masses of dwarves means you most likely have dwarves with all the labours you need (game ensures the labours you need are enabled in migrants). So you can do anything you want in no time.
Automate food and booze production with your manager and you never have to worry about it again.
Biggest mistakes to make are to think that Dwarves enjoying themselves and not working is a bad thing (the opposite actually) and that you have to micromanage labours (no need with a fortress packed full of dwarves unless you actually want to start optimizing projects).
What's the problem again?
A good sized plump helmet plot, a dormitory, a dining hall, and some dedicated brewers / farmers is all you need for a heck of a lot of dwarves to get by just fine. Seems like no matter what, some tend toward insanity, so I don't really bother with amenities at first. Running out of booze and food will cause greater unhappiness anyway. If you have these basics, then you can pursue other aspects of the fort at your leisure.
I sometimes will put everyone in the fort on food & booze production for a couple years to build up a massive stockpile and then not have to worry about it at all for several more years afterward. Also, with a massive stockpile of food and drinks on hand, it doesn't matter how many migrants arrive, and they can be put straight to work on the current project.
Having dwarves idle in the meeting area gives them a chance to meditate, socialize, sing, dance, etc. which keeps them happy. But it's also a sign that you have untapped potential to get things done. If I have a bunch of idlers, they can almost all be put straight to work by giving them some common labors:
Stone Detailing: And smooth a bunch of rooms, engrave the dining hall rooms, etc.
Weaving / Tailoring: Once you start growing pig tails, you can keep 5 dwarves fairly occupied constantly making fresh clothing to replace old tattered rags
Miners: Why not make some exploratory tunnels all over? (Just make sure to wall off the caverns when you find them)
Construction / Masonry: Surface constructions take a lot of blocks and a lot of construction dwarves. Even a simple walled courtyard with covered fortifications along the walls takes a lot of dwarf power
If you have a lot of stones, enable stone hauling on everyone and make a few big stone stockpiles. Then crank out rock pots for days. Doors too. I
always manage to run out of food storage and doors multiple times in every fort.
That's all just basic stuff though. If you have a particular goal or project in mind, just start it. Then when it's not done instantaneously, look to what isn't getting done? What needs to be done in order to get to the next part of it? Then give a handful of dwarves that particular labor and nothing else. Rinse and repeat until your tavern is empty.
Edit: a Suggestion - Perhaps the first big project could be digging out the rooms for a large population fort. It will take some planning, but if you have a big plan, and that plan is simple and clear, then you will not feel like you have enough dwarves.