I've got a '92 Lumina, it's on the same platform as the Regal, a "W" chassis, and it's just rolled over 210,000 miles, and the only thing I've done to it are the normal maintenance items. It's got the 3.1 V6 in it, and it runs great. I bought it with 106,000 on it back in '03.
I've also got a '96 Monte Carlo with that same 3.1 V6 that a friend of mine had. His wife drove it 200 miles a day to and from work, and right now it has 257,000 on it. The transmission finally went out, the reverse doesn't work now, but I did all of the maintenance on it for them too, and it's never needed anything more than a water pump and an alternator. I bought a transmission for it over a year ago, but I haven't been able to put it in yet. My health problems are what's preventing it right now.
But if you are looking for a reasonably priced, used car, try any of the GM W bodied cars, the Buick Regal, Chevy Lumina, Pontiac Grand Prix, or Olds Cutlass. If you get one before 1996, it will have the older computer system on it, and the diagnostic tools are cheaper for them, although the '96 and newer OBDII computers will tell you more about what's wrong with the car on a diagnostic tool, you have to have that tool to get anything out of the computer. With the older system, you can just plug in a simple coin tool to the diagnostic connector, and the comp will flash codes with the service engine light. Then all you need is a chart to tell you what the codes mean.
If you are mechanically inclined, you could do that easily enough.
Good luck in your search.