I've found a hotel in each of these places, both equally meet my needs. Please can someone advise me which location is the best?

Also, I can either spend 2 or 3 nights. Which do members recommend with regard to sightseeing?

Many thanks.

p.s. I won't be going in a hot air balloon

I went there 2 times, and I stayed in Ürgüp. I think Ürgüp is better for staying, it's more lively and sympathic I guess. you can go to Göreme to do some sightseeing later.
The Göreme open air museum where there are many small churches and the underground city (ı forgot where it's) are a must see. Anyway it's a small place, 3 days will be enough to see the surrounding.

Goreme tends to attract a slightly younger crowd. Urgup is slightly bigger. But both are centrally located and either place would be good. I know you said you don't want to do the hot air balloon but it is absolutely spectacular. I am afraid of heights and I loved every second of it. I would recommend visiting the Soğnalı Valleys -- great hiking, interesting crumbling churches, lovely scenery and I did not run into a single visitor the the whole day I spent there. As for how long to stay I could stay there for weeks but I love hiking around and exploring. I think you can easily see the main sights in 3 days.