Perhaps I'm partial, but Odessa is simply beautiful. Discovered by the Greeks, founded by the French, and for years an independent port, the city is busting with cultures from around the world. Although, the people tend to like their own. However, don't let this turn you off to the city because people still act nicely and the American hand is evident in the city. While walking down Deribasifskaya, the main street through the city, I saw several American stylized restaurants, including an Irish pub!
The city isn't what it used to be. Due to lack of funding, parts of the city are completely decrepit, but other parts looks like a part of western Europe. You can buy anything you want, they sell most American products. Most natives can't afford this, but it's a great deal for a visitor.
I wouldn't recommend going to the circus because the dagger tosser could barely hit the target, let alone the bull's eye, the animals were malnutritioned and misbehaved, and most of the animals that they used were domesticated animals rather than exotic ones. There were some good parts to it, but not worth sitting two hours in the stifling heat.
Odessa is pretty hot in the summer. It's usually in the mid to upper 80s and it's humid. Some stores are air conditioned, some not. And the public transportation is not cooled. You might be lucky to find a taxi that has it. Taxi's in Ukraine aren't just from taxi companies. They use a sort of hitchiking system. You stick out your hand and any passing car that wants some extra money will pick you up and take you where you need to go. Haggle with them. Haggle with everyone.
Something to know before you go: Odessa is known throughout the former USSR for two things: 1. A biting sense of humor so go with a thick skin and a sharp tongue, and 2. Beautiful women so don't stare.