Kusadasi & Marmaris have a lively Bar Street. Kusadasi probably more so!
Bodrum doesn't, however it's only 10 minutes away from Gumbet and the nightlife there is great! So you have 2 resorts to choose from.
Bodrum does have 2 of the biggest and best clubs though. Halikarnas Disco & Catamaran Club - the disco that's on a boat. I loved them!
I wouldn't advise staying in Bodrum itself though, because you will end up spending most of your time in Gumbet as all the good bars and beaches are there.
If you want to do some sightseeing Kusadasi is very close to historical wonders like Ephesus and Virgin Mary's House.
Also you can book a day trip to Pamukkale, which is lovely.
Bodrum has the old Castle and other historical sights.
From Marmaris you can go on a trip to Dalyan/Caunos/Turtle Beach where you can see Caretta Caretta Turtles and have a Mud Bath.
The beach in Marmaris is not very good, it's very narrow and the sand is mostly black and a bit gritty...but you have the added bonus of being very close to another resort - Icemeler which has a much better beach.
The Beaches in Kusadasi are nice, there are many to choose from and they're all accessible by dolmus.
Bodrum bay beach isn't very good, but Gumbet's is lovely and has a wide variety of watersports.
All 3 resorts have trips and excursions such as jeep safari, Turkish Night, Turkish Bath, Horse Safari, village tours, Boat Trips etc.
I think you'll have a great time wherever you go though.