I get over to Slovakia every other year or so to visit cousins and I agree completely with opushomes about Bratislava. It's a great city to visit, but you can complete most of the things to do there in a day or day and a half. I enjoy just walking the city and the parks and gardens are quite beautiful. If you are spending more than a day, try to get to the Botanical Gardens.
If you are thinking of taking the Hydrofoil from Vienna, be sure to get your reservations early. It's a pretty popular trip and was sold out several days before we wanted to take it from Vienna to Bratislava several years ago in late September or early October. The train isn't a bad trip, but getting from the train station to anywhere near the tourist areas can be a challenge.
Kosice is another city that you can see pretty much in one day, but I still love visiting since the people are quite friendly and the food is good. There are several restaurants on the main street in the historical center and always seem to have quite a few people having dinner. The prices are also reasonable. I generally end up at one which I like (I think it's called Restaurant 12 apostolov).
One tip from my cousins... If you are driving through Slovakia, don't speed. The police give tickets for 1 mile over the speed limit and will expect you to pay immediately if you are a foreigner...
Enjoy your trip... It's a beautiful country and the people are great.