Don't just stick to the village. The Upper East Side has some great places. Mad River on 3rd avenue and Bar Harbor(I forget where it exactly is) are two of the best bars I have been to.
Mad River is awful!!!
I am not sure when you went, but its has been bad for a while now.
I live like 4 blocks from it and its full of stupid frat guys and equally stupid overdressed bimbos.
Unless you like that sort of thing.... And its always packed, with a line outside.
I will never understand what attracts people to that place. but I am not a fan of overcrowded places...
1. Just explore. You dont really need a plan. There are hundreds of bars.
2. What Dsong said... it isn't cheap thats for sure.
3. I dont know about law students, but everyone pretty much goes out all the time...basically whenever they can afford it. i.e. people are out basically any night you go out.
4. "entertainment"? You whave to check craiglist...or the back of the village voice.