Kevin. Check out yelp or google. I was there a couple weeks ago. I only went to one place. Cigar Republic in Treasure Island. Very small but friendly.
They have a line of cigars made for them in Nica and Costa Rica. Bought a bunch but haven't tried them yet. Certainly look and smell good. They have drinks.
There's a great dive bar about 5 doors away closer to Gulf Blvd. Lana's Place. Friendly people, extremely cheap, and you can smoke. It's not fancy at all, but I felt safe.
Tampa and Ybor City are close. Ybor is an awesome cigar destination. Oh I hope you didn't mean the city in Russia.
Can't help ya there.