Lots of good suggestions. I'll only comment on the cars I've owned:
- '95 Miata 1.8L: Bullet proof car, you probably wouldn't have to repair much but a few things are a pain to get to, e.g. CAS seal and even the oil filter. Overall not too bad
- '88 Volvo 240: Fairly easy to work on, pretty reliable except for the fuel pump relay, wiring harness issues on the older models as well as the blower motor and heater core being a total PITA to replace...step 1. remove the whole dash board.
- 92 Integra: again, not much goes bad and actually fairly easy to work on.
- '88 Corolla: Fairly accessible engine bay unless you've got issues with the crazy electo-magical carburetor...avoid it.
- '91 NSX: Very reliable, I didn't have to do a thing and despite being mid-engine it wasn't all that hard to do basic tune-up stuff.
- '87 MR2: Again, not that hard to do but probably better to avoid mid-engine cars since most of them require lifting the body to drop the engine out from under the car. Fun to drive and reliable car though. I enjoyed it more than the Miata.
- '88 Supra: Forget it...miles of vacuum hoses and head gasket failures.
- '86 Jetta: Pretty darned easy to work on actually, the 1.8L 8v engine is pretty simple and basic
- '65 Volvo: It was a 3rd car...my wife (in her mid 20s then) wanted it so we got it. At the time I only had a $20 tool set from Autozone and I was able to do anything that it needed. I didn't get a chance to take it all apart as I'd planned. We sold it after about 2 years.
- '92 Dodge Dakota V8 with 318: There's fair amount of room around the engine but some things on the engine are a PITA to get to e.g. thermostat, oil pressure sending unit even the distributor is way back right up against the firewall.
- '97 E36: Mechanically solid car overall, cramped engine bay but surprisingly DIYer friendly. I've replaced every suspension bushing, differentials, radiator, clutch, tune-up stuff on it myself without having done some of those things before. As long as you have lots of wobble adapters etc you're ok.
- 04 Accord 2.4L: Bought it brand new for wife with the intention of passing it on to our 6 mo old (at the time) when she's 16. The engine bay looks fairly easy to work on but we haven't had to do a thing except brakes pads, rotors, tires, battery and oil changes. Uses timing chain so service manual calls for major service at 100k for ATF changes etc. With almost 60k I'll be changing all the fluids soon.