I don't know what sort of night life you are looking for, but there's not much for the tourists in La Romana. There are several discos in town, but they are geared much more toward the local crowd.
As far as AIs in La Romana? I think the Casa de Campo resort has an AI option and it is very nice, but very expensive.
Not much night life there to speak of. There is a Disco (Genesis? I think?) at Altos de Chavon which is a short drive from the hotel... very nice on the weekends, party doesn't start until waaaay late, though.
Maybe you should look into Bayahibe about 20 or 30 minutes away? There are several AIs there, beautiful beach, and I think you'll find more of what you are looking for. You can always head into La Romana for a day trip...
www.vivaresorts.com has 2 hotels (Dominicus Beach, and Dominicus Palace) there that always seem to be busy when I am down that way. There are SEVERAL other hotels in Bayahibe, but I don't know the names off the top of my head. Do a google search and I'm sure you'll get the rest of the names.
Good luck.
Tim