I own a 1998 A4, 2.8 Quattro, manual as well as a 2001 Allroad 2.7T, Quattro manual. Maintenance and repair costs should be comparable to other German makes, and generally higher than Japanese makes.
Timing belt replacement can cost less than a grand. I think I paid $700 to have the dealer replace the belt on my A4 a couple of years ago. The local Audi dealer labor rates did increase from $80/hour to $110 since then. It is harder to find a competent independent shop to work on your car since German cars are so much more complicated compared to Japanese and American models of the same year. If you can find a good independend shop for repairs and maintenance the ownership costs will not be that bad.
That said, if you are looking for a hassle-free experience you may wish to look at a car with an extended warranty or a recent model year still under factory 50,000 miles warranty/free maintenance plan. The free maintenance was discontinued for 2007 on Audi models though.
I highly recommend you read model specific forums here to get more of a feel for problem areas for the particular model year you are considering.
Audi World
If you are looking at TT there are the more powerfull 225HP/quattro models you would probably like better than 180HP/FWD model. You may also want to check out the special "Baseball glove" interior which some TTs come with which is just gorgeous.
With Audi a lot of problems are common to a particular model and year. For example, the B5 generation A4 usually need to have most of their front suspension bushings replaced at a cost of a few hundred dollars.