With my brother I traveled from Kiev to Odessa by night train. The train ride is about 9 hours and cost approximately 10 Euros. We had to share the compartment with 2 other people, which was fine. Luckily the man and woman could speak some English, so we could have short chat.
Odessa wasn't the first place to think about to visit in Ukraine. My flight back home was from Chisinau, Moldova and the easiest way to get there is via Odessa. Odessa is a harbor town at the black sea. During summer you can find many nice beaches to relax. It is buy then, but the atmosphere is great!
We had one day to explore the city. It has some nice buildings like the Opera and churches, but the best to visit is the market. The very huge and lively market is selling food but also clothes.
I did noticed that during the Winter many buildings where under constructions. Also the famous stairs only had a small path to climb up.
I'm gonna take you to Odessa with a photo essay.
The most cheapest way is by night train from Kiev. The ride only takes 9 hours and you'll have a bed to sleep. There is also a fast train, which takes you there in about 6 hours, but that one will arrive after midnight.
During Summer you can either take a train or a bus to Tiraspol. This runs every day. During Winter the train only runs on Saturday and Sunday.
The bus leaves every day at 7 AM and 7.30 AM from the international bus station in Odessa. It takes you to Tiraspol in about 2.5 hours, including the border check.
During the border check a customs officer comes inside the bus, takes your passport and put the exit stamp from Ukraine. At the border of Transnistria you have to give an address to the customs officer, then go to a small office where they print your 24 hour permit receipt. Keep this with you all times and you have to return it when you leave the region. All in all it only takes a few minutes and is really easy.