This was my second time in Santorini. My husband and I stayed in the village Imerovigli, which was absolutely wonderful. It is just as quaint and romantic as Oia, but not nearly as crowded, and a bit more affordable. It is also close to the main town Fira, and easily accessible by bus. We had a perfect view of the caldera, volcano right in front of us, and Skaros Rock to the right. Our hotel, On The Rocks, was out of this world!
I would highly recommend staying in Imerovigli if you are going with your significant other.
During our 3 days in Santorini, we went to Oia, walked around Fira a bit, did a volcano & hot springs boat tour, visited the archaeological site Akrotiri, and briefly went to Kamari, one of the black beaches. FYI - it is not sand, it is large pebbles.
3 days was enough to do all the main things, though one could easily fill up a week. However even if you only have one night to spend there, you can do the absolute "must" things in that time.