First, A4s seem to be good cars that provide a lot of usable mileage. I've had two good friends who own/operate repair shops that specialize(d) in European cars and yours is a fairly common question. Audis, BMWs and Mercedes are complex cars, so it's important to find a shop or dealership that you trust BEFORE you buy. They also agree on a budget number. The two guys agree that an owner who does none of his/her own work should budget an average of about $2,500 a year for service (tires, batteries, filters, oil changes, fluid services, etc.) on a properly maintained car. Also, be sure to talk to your insurance agent in advance to get a firm number for the coverage you want.
Edit: Another bit of advice is to join an on-line forum for the car of your choice now - before you buy. Reading the day-to-day comments of current and past owners will give you excellent insight into a car's general reliability and probably highlight common problems. I like vwvortex.com - they have sub-forums for virtually all VW/Audi models and have a large, world-wide audience.