I've had my 02 A4 for 3 years and although it was due for a Timing belt and related equipment update, not much else has gone wrong with it mechanically. Make sure the timing belt has been done, also the plastic impellar on the oem water pump breaks up causing heating problems. If the water pump has been done or needs replecement, make sure the water pump is replaced at the same time as it requires timing belt removal to do so. Might as well pay the extra $70 while you're in there rather than wait until it fails.
I've had a few surprises when the coil-packs go without notice but have learned to have an extra one in the glove box in case of failure. You'll know when you blow a coil pack as the car will begin shuddering (running on three cylinders) and the engine light blinking. Doesn't happen very often but it helps if you're prepared. I've had two go in three years. Check with an Audi dealership as the 02 A4 has coil packs that are replaceable under an Audi recall. They'll replace them with new ones for no charge as long as they are OEM and fall under the recall models. I would advise to buy one extra to keep in your glove box just in case. They're only $50 or so each.
I've also replaced the window regulator on the driver's side as the cable was worn out and fraying.
Other than that no major problems (knock on wood). I've heard of a few comments on how unreliable the first release of the B6 is, but personally I think they're fine. It seems that the reliability issues can crop up no matter what model of Audi is concerned as they jam so many extras into these vehicles. Overall I've had a great experience with my A4 and will be upgrading to another Audi asap. I've just put mine up for sale if anyone's interested!
As for the Rad issue, I'm not sure of cost of replacement but I do know of a great site where you can get OEM parts at a great price:
genuinevwaudiparts.com
I've bought all the things I've needed from them over the past couple of years. Great service, they run out of a dealership in California.
Hope this helps, I'll try to answer any other specific questions if you have any.