$20,000 would buy you a nice
new Ford Fiesta. I priced one up and you can get a Fiesta SES (top model) with leather seats for $19,440.
I own one of these (European version) and I have to say it is by far one of the best all-round cars that you can buy. Sure, it is not going to win any races, but you are surely getting this car so you can travel to the new job you will get after University. The interior is very nice (best in class I'd say), the stereo has great iPod integration and there is lots of room in the back and trunk.
It definitely satisfies your "fun" requirement - the handling is great and it is a joy to drive. I'd also say it's quite respectable - people who know anything about cars know this is a good one.
Also as a new graduate, why do you need a big sedan? I'm a relatively new graduate too, and I drive around in my Fiesta with 4 empty seats most of the time - what use would it be to have an even bigger car?
It's also not AWD, but who really needs AWD? FWD is fine in all but the most extreme weather conditions and I am still yet to meet anyone IRL that actually ever drives off road on a regular basis.
It's a small car, so the running costs are low. The parts are cheap and very easy to find and consumables like tyres are also very cheap.
Here are a couple of pics of mine from the "post your car" thread in the Picture Gallery forum.
Avoid used German cars unless you get a bulletproof warranty!!!! That $20,000 sticker doesn't include the thousands you will end up spending on maintenance and repairs.