There is neither an airport not a seaport in Transnistria. Tiraspool, the major city is landlocked and is largely shut in from the outside world due to a lack of transcontinental infrastructure. The closest airport is located in neighboring Moldova. It is an international airport, however, there have been many nations that have implied 'travel bans' on both Moldova and Transnistria.
Transnistrians do not have ready access to the Internet. About 5 of 100 homes have access to the world wide web. Most of these homes belong to the cultural and political elite. The government has limited the rights of free speech and thus is not apt to embrace technological change and development. The local sewer system and electrical grid is state of the art. Recently adapted from models based in western Europe, the Transnistrian basic infrastructure was built in the mid 1990s after the profits gained after the war of independence in 1992.
There is regular bus and maxi-taxi service to Chisinau, Bender, Causeni, Odessa, and other Ukrainian and Moldovan cities. The main bus station is about a kilometer from the city center and has clearly posted schedules. No visa or payment is required for EU, Moldovan or US citizens when staying for less than three days, but you must remember to register with the police unless you are just on a day trip. Some people have reported getting shaken down for payments at the border - if this happens, hold your ground and act stubborn and clueless. Many more people have crossed into Transnistria without any hassle.
You can see most of what there is to see in Tiraspol by walking up and down October 25th St., the main drag. There are several nice parks in the city, including the Culture Park near the university. This has abundant trees and a mixture of abandoned and enthusiastically used amusement park rides, and is a good place for people-watching. Most of the big monuments are at the south end of the city, about 2 km from the Palace of Soviets.
In order to purchase goods, services or souvenirs in Tiraspol, or in any Transnistrian locale you must exchange your outside currency into Transnistrian rubles. The Transnistrian central bank sets their own exchange rate and prints their own money, so the amount of rubles you will get on any given day for your euros varies significantly from week to week. Currency exchanges are everywhere, including inside many popular stores, and will change most local and major currencies. You can't pay with credit or debit cards in Transnistria.
There are many shops and markets to purchase local food, drink and their famous Transnistrian Vodka drink commonly referred to as a "smirnovka" - appropriately named after president Igor Smirnov.