Definitely hit up Resort one night, it's located in City Place right next to Barnes and Noble. They usually have something goin on every night but Saturday is the best.
Bradley's is lots of fun if you're in your early-mid 20's and want to get laid. Tons of chicks there and you'll see a lot of them dancing on the bar by the end of the night. It's located at the end of clematis on flagler, just off the intracoastal.
Blue Martini in City Place has a good atmosphere, check it out on a Tuesday for Tall Blonde Tuesday's (ladies night) I'd recommend having dinner at City Cellar and hten heading over to Blue Martini for drinks.
I've heard Sin on Clematis is a nice place but haven't been yet.
The Waterway Cafe in PBG has the best Sunday night entertainment. Waterway is a island restaurant located on the Intracoastal (floating dock bar and everything) that has Reggae night on Sunday's.
If you can't make it up north for that, Gatsby's in West Palm has Service Industry Sunday's which are casual and laid back + free buffet.
For other restaurants, Tsunami is an Asian fusion restaurant located @ CityPlace. Quite expensive but I've heard the food is great.
If you head over to the island, check out Cochinas(?), it's a quaint little wine bar that has some nice tail running around.