a lot of the cheaper hotels in Trabzon are full of “natashas”, prostitutes from the former Soviet Union, so it is worth paying a bit extra for a hotel which advertises itself as an “aile” or family hotel. there is a good place called Hotel Nur, just off the main square (ataturk alani)...but as it is small, it is often full. Next door is the hotel Benli, which is cheaper, more basic, but friendly enough.

Hope this helps :)

www.virtualtourist.com is also very useful for this sort of question