There is a good system of trams running through the city.
The most interesting thing to see in Odessa is the old town itself. The city was once the center for trade coming into the Russian empire and as such has much of the grandeur of a wealthy city. Conversely though the city appears to have had no upkeep since the 1917 October revolution and has had even less since the end of Communism in 1992. As such, vast portions of what was a magnificently wealthy old city are falling into a state of total disrepair. The old section of the city though is quite clean and feels very safe so it makes for a good two days worth of casual unguided wandering particularly with the wide tree lined avenues and large open parks.
In the much smaller and more well well kept part of the Old town there is a large Opera house and some very nice parks. There is also one main street leading through the old town that is vibrant with people selling street goods to tourists.
The price for food is very cheap (under 2 USD) so long as you don't eat in any restaurants owned by wealthy famous Ukrainians, in which case the prices are extremely expensive. The 'fast food' on the street is particularly tasty and if you don't speak Russian or read Cyrillic is much more accessible as you can just point at what it is use want. Menus without exception, in normal restaurants, are exclusively in Russian so either have an idea of what you want before you sit down or be prepared to randomly pick something from the menu.
Avoid food from street vendors esspecially at the open air markets. The food quality is questionable so it is wise not to take chances. There are several supermarkets in Odessa that have high quality foods that you can buy as an alternative. There are several Mcdonalds resturants in the city.
The beer served in the south of Ukraine is outstanding and goes excellently with the hearty food. In the words of one not so impartial citizen of Central Europe who visited the country, 'Hey, this is as good as Czech beer!?!' A beer in a restaurant will usually cost around 0.50 USD.
Most wine that you order in restaurants will be very sweet.
Accommodation is plentiful in Odessa and ranges from renting a small hotel from a local resident to more expensive hotels. If you enter by train you will be immediately approached by one of the many locals in an attempt to get you to rent a room from them. This may end up being a small not so well constructed (but basically clean) one room structure located in their garden. It may also not come with a shower with running water, instead consisting of a small outdoor cabinet with a tank located above it that your host will fill with hot water upon request. Additionally the local accommodation will most likely have a Turkish toilet. For those uncomfortable with using a Turkish toilet the facilities at the McDonalds near the train station make for a good substitute. Note that nobody speaks English or German (even the most basic talk). This makes the negotiations very difficult! In july/august most budget hotels are fully booked off. For medium budget travellers the best option is to book an apartment on internet in advance (rates 40/60 euro.
A new Hostel has openned in Odessa, Black Sea Backpackers, who offers dorm beds for arround 15 USD. (listed on Hostelbookers.com)
It is recommended though that you bring your own sleeping bag and small camping pillow as the bedding is not frequently changed.
The total price for your garden residency will usually not exceed 10 USD and in the summer it more than suffices.
If you are going to the Crimea it is a 12 hour overnight train ride costing somewhere around 10 USD (2 persons sleeper 25 USD, very nice!) . If you buy your ticket on the day you are leaving (not recommended) there is one group of cashier windows where you buy your ticket in the train station. If you buy your ticket on any other day (i.e. at least one day in advance) there is a completely separate group of cashier windows where the ticket must be purchased. As the lines can take up to 30 minutes make sure you are in the right one. Nobody in the train station will speak any international language. In Simferopol you can take a trolleybus to Yalta via Alushta. The beaches on Crimea are in summer awful crowded and the beachresorts are very noisy. Its better to go to East Crimea on the Sea of Azov.