No, you guys, this is not because I am an alcoholic. I don't drink in America, mostly because it is still not legal for me, and partly because I think beer smells terrible. Actually, the funnest part (the part that is most fun?) of the nomikai is the 会 (the meeting).
I suppose if you're in a club you get to meet with people so many times a week, every week, but the focus is on the activity, so you don't really get to talk. Or maybe like me you are super awkward and it's difficult to talk. The atmosphere of a nomikai is great for social awkwardness, I think. It's relaxed and people are just there to talk and have a good time. Attending a nomikai can help dispel any lingering sense of 'otherness' or 'outside-ness' that you may have.
What can you expect from a nomikai, besides good food, tasty beverages, and good company? In my experience the nomikai is usually held in the following format: a 2-hour all-you-can-eat, all-you-can-drink party (たべほうだい・食べ放題、のみほうだい・飲み放題）, in place of dinner time. Depending on where you go, the price will vary, but for both all-you-can-eat (tabehoudai) and all-you-can-drink (nomihoudai), you can probably expect to pay between 3000 and 5000 yen (around 30-50 dollars).
A variety of restaurants offer this option (places like izakaya, for example) or specialize in it, so whether you want to tabehoudai at some Okinawan food or some good ol' yakiniku, you'll be able to find it. From the little that I've seen in my limited experience, drink choices are pretty similar throughout, for those who care to drink as well. If you're 20 or over, besides juice, tea and soda, you can choose from a menu containing cocktails, sours, beers, wines, and hot/cold saké. The window for nomihoudai usually closes after about 1 hour and 30 minutes, and once your two hours are up you've got to get out of there.
That's the only downside - even if you want to just hang out a bit more after you've stuffed yourself with grilled chicken and Cassius soda, you've got to get out of the establishment. This means everyone goes home at around 9pm, well before trains stop running. OR if you want to have some more fun, you can go to another place for phase two of the nomikai. (Yes, another round of stuffing your face. I can't believe I thought I would lose weight in Japan). The next option: you can go for some karaoke - also another great way to spend time with/get to know people. (Actually, if you spend too long looking for a second establishment, and then spend your two hours there, you might just miss the last train, in which case you have to do some all-night karaoke, unless you want to pay for a hotel/capsule room/manga cafe to sleep in.)
It's kind of like hanging out at a barbecue, even if you aren't grilling skewers of chicken over the fire in the middle of your table. Everyone is relaxed and laughing. You have time to sit back and hear about people's lives. You make fun of the drunkest people there. You exchange phone numbers and email addresses. People are friendly, but sometimes they're too busy or shy to get to know a person, and ask the questions they want to. Nomikai are kind of a event for that. I've had a lot of fun getting to know people at nomikai.
I'm going to miss all of them.
Attending nomikai may result in lost shoes, and
necessitate piggy-back transport.