- don't say "fast" you're not going to get a real fast car with 11K unless you buy something cheap and put a toonnnn of work into it. Anyways, some ideas.
VW GTI or Jetta - don't not get one just because your friend has one. i have it, it's a nice car. 1.8T is easy to mod, a chip will give it 205 HP right away, a stage 2 chip with intake and full turboback exhaust, you're looking at 230 HP. VR6, quicker than the 1.8T, sounds waayyyy better than a 1.8T, but can't be modded much without putting a lot of money into it. Seriously look at these cars though
Toyota Celica GTS - My buddies got one, definitely in your price range. It's not turbo, but it has lift, kind of like a VTEC in the higher RPMs. It's a fun little car.
Chevy Cobalt SS (/SC) - I'm not sure if the prices are down enough on them. But these are excellent cars. I was allowed to test drove a SC overnight, so I drove the pants of that thing. The drivetrain is amazing, it feels way faster than it is, clutch is smooth, supercharger doesn't let out. If you have the money, seriously check this out. If you don't have enough, maybe test drive an SS NA. It's still a 4 litre, but it's quick. I know a kid who just has an intake, exhaust, and a modest nitrous kit, he's pretty quick.
Mazda 3 2.3 litre - Not too shabby. It's won a ton of awards. I'm not sure you can mod it much... but mazda's have super light clutches
Mitsubishi Lancer Ralliart - Not Oz Rally, Ralliart. Faster engine, Evo style suspention and transmission. kinda hard to find, but at least it's rare
Ford Focus SVT - Looks nice, 6 spd :), has lift, rare. Fun fun car.
Honda Accord V6 - not my favorite, but it's an idea
Honda Civic Si (2002 and 03)
Acura RSX type-s - good luck finding one in your price range though.
Dodge SRT4 - quickest thing quarter mile in this list. It's a neon with a stupid fast engine. Not my style, but it's quick.
Ford Mustang V6 - RWD, sure a ton of people have one, but it's not that bad. girls like them too, so bonus points there.
There's some ideas. My top 3 on the list would be 1) Cobalt SS/SC 2) VW GTI 3) Focus SVT
Good luck. any questions just act.