I can't remember any of the names of the places that we went to in Bodrum unfortunately
but Gumbet is mainly cheesy type stuff.
I'd definately recommend going to the Outback bar in Gumbet (go to the very top of Bar Street, turn left, and it's 100 yards furthur along, across the road) The cocktails are lovely, and the style of the place is very much chilled out (rock/indie/alternative music) which is sooooo different to most of the other bars.
A nice area of Bodrum is up by the Marina. The restaurants there are a bit more expensive that the rest of the resort, but you get what you pay for, the food was delicious.