Getting to Tiraspol: It's easy enough. The bus station is right beside the Central Market. Buses to Tiraspol leave every 20-30min. I found the bus with the Tiraspol sign on the front, and the driver walked me up to the window where I paid for the ticket. I believe it was just under 37MDL (around $2).
The drive was bumpy because roads in Moldova aren't great, but luckily it's only about an hour.
At Bender, you have to cross the Transnistria border. There were 4 other people on the bus and they all had passports that allowed them into Transnistria without a visa. Since I have a US passport, I was required to get a permit/visa (free cost) that allowed me to stay for 24hr. I walked up to a window where the guy took my passport, entered the information, and gave me the paper permit/visa.
Afterwards, he handed me the passport and said to walk with a guy in military fatigues. The guy looked at my bags in the bus, said OK Good, and then took my passport up some stairs. This is when I got worried because my passport was no longer in my possession. He came back about 10min later with my passport. I still have no idea why my passport was taken.
Tiraspol: The train/bus station is just north of the city. It's about a 10min walk from the main part of town. I arrived shortly after 12PM and had heard that buses to Odessa fill up quickly, so I asked to buy a ticket for a bus that left around 5pm. Unfortunately that one was full, so I was stuck in Tiraspol until 7PM.
Tiraspol does have a tourist office now! It's on the road leading to/from the train/bus station, about halfway towards the main part of town. The ladies working there spoke English and gave me a map in English. They also sold some post cards and other souvenirs (which I doubt you'll find anywhere else in town).
Also, since Transnistria isn't an officially recognized country, you can't use debit cards or credit cards and as far as I know, there aren't any ATMs that will work. I brought Moldovan Lei and was able to convert them to Transnistrian Rubles at exchange booths that are all over town. I didn't even have to say anything; just hand them the money and they know what to do.
I have T-Mobile in the US and get free roaming in many countries. However, my roaming did not work in Transnistria. Fortunately, I was able to get cell reception from Moldova in certain parts of the city.
Highlights were the House of Soviets with the giant Lenin statue outside
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A Soviet era movie theater
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A Soviet tank
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And another Lenin statue in front of a government building
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I also went into the Sheriff supermarket which is owned by a former KGB guy. The Sheriff brand is also a soccer team and a large hotel in Tiraspol.
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The Kvint distillery in Tiraspol is known for producing cognac, vodka, and other types of spirits.
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There really weren't many advertisements in Tiraspol except for local related things. Absolutely no capitalism here.
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Overall, Tiraspol is an interesting place to spend half a day. It gives you a glimpse of what life would be like in a modern day USSR.