Ellen,
I did some of those ports on the Diamond last summer. So ask questions if you like about Yalta, Sevastopol, Odessa, Constanta and Nessebur.
We did the Radisson excursions in these places, but I'm sure there are private guides. I found it difficult at the time finding info on the net. I think Nessebur would be quite easy to do on your own, if you wanted to tour the old town (as we did.) In Constanta, we took a tour to Ancient Histria, a Greek settlement at the mouth of the Danube. Beautiful.
The Ukraine is crawling with former-soviet Intourist guides. I found some of these tours tedious, since they were very regimented. We went to the palace in Yalta where the famous conference was held, had to wear slippers to go inside, and were herded like cattle. Yalta is very touristy, not all in a good way. Odessa is beautiful. We had the good fortunate in Sevastopol to have a Crimea history expert onboard who led the tour, but there seemed to be good local tourism support there as well, very well worth the visit.
Let me know if you want any specifics about these places.