You can hire a classic car (comes with driver) for any tour or transfer in Cappadocia.
There is a maximum limit of 3 persons per vehicle.
You can go sightseeing for 2, 3, 4 hours or full day. The driver will take you to pre–arranged sights.
If you want a tour guide, this can be arranged as well (the maximum limit with a tour guide is 2 persons).
Are you planning to propose over dinner? Going by classic car would feel even more romantic ;)