In 1993, Slovakia peacefully divorced Czech Republic and has been somewhat off the tourism radar. But being one of the cheapest countries in Europe - it's only getting more and more popular.
Bratislava
The capital is a pleasant city. It has a castle and a few cute town squares, but doesn't merit more than a weekend. Head out to Pezinok 20 kilometres away, to watch a game of hockey, just don't suggest to the locals that the Slovak national hockey team might not be the best in the world. A sure good way to make friends with Slovaks is to make fun of Hungary.