I did some of these with the family a couple of years ago.
Konya - if you're interested in prehistory take a trip to Catalhoyuk, billed as the world's first city - it's about 10,000 years old. Public transport is sparse, so we got our hotel to arrange a taxi to take us out there, wait for us and drive us back. If you're there at the right time (we weren't) you may see archaeologists at work. Some of the finds are in the museum in Konya, but signage there is minimal, even in Turkish, never mind English, so it's good to see the actual site first. Other finds are in the archaeology museum in Ankara, which is superb.
The Mevlana complex is also worth a visit.
Ankara - archaeology museum, as already noted. The ruined castle has fantastic views. We didn't do the Ataturk museum, but I wish we had, as everywhere we went people, even schoolchildren, treated him as a hero, so I'd have liked more background.
Cappadocia - don't miss the balloon flights. I thought they were mega expensive and wasn't fussed, but DH said we should do it and I'm so glad we did. Absolutely magical.
Someone said to hire a car - we didn't and got around very easily. I don't think we even got buses, apart from a tour bus for the Green (I think) tour, which was a day and was worth doing. We had a couple of hikes in the valleys (Love Valley, Red Valley, Rose Valley) and you can walk through the valleys to Uchisar. Routes are not well signposted, so make sure you can figure out where you're going.
I forget exactly where they are, but look out for the gravestones with a date of birth in the Hijri calendar and date of death (post Ataturk) in the Gregorian calendar; it looks like they lived for hundreds of years!