I ran an 80 Avant TDI SE for just over 5 years/100k miles until Oct 05 and have to say it was one of the best cars I've ever owned......
Serviced it religiously with all genuine filters etc and fully-synthetic oil, had belts replaced at manufacturers intervals and sold it at 213k miles running like a proverbial Swiss watch......only sold it to buy the A4 which has aircon!!!!!!
Economy was 45-48 mpg during my ownership (I always fill the tank to full at every fill-up and keep a little book in glovebox where I note car mileage/fuel used and distance covered.....)
Compared to the A4 the 80 (in my opinion) is better built and doesn't seem to suffer the minor electrical glitches that the later Audis have.....
The only issue I found with the 80 was that it was very heavy on front strut-top bearings.
I replaced the lower wishbone bushes with Powerflex polyurethane ones and they stiffened up the front end considerably, but the strut-top mounts are no different (as far as I am aware) to those used on smaller VAG-group cars like the Polo/Golf, so they take a right hammering on the relatively heavy diesel-engined 80....
Consequently I was going through a pair of strut-top bearings at literally every MOT, given I was doing approx 20k miles/year, (and yes, Genuine Audi mounts were being used ), the only good thing is that as the later (think post 1990?) 80 suspension struts are in 2 pieces its quite an easy job to whip out the suspension leg to change the bearing leaving all the hub/brakes etc in place, but you do need the correct tools eg coil spring compressors to do the job!
I did fit a pair of uprated mounts from an ur-quattro one year but by the next MOT they had gone again!
Dont let this put you off though, if you can do your own DIY the 80 TDI is a fantastic car, look after it and it will last (virtually) for ever!!!!!!