In Slovakia make sure you validate your tickets if you take the bus or the tram thingie (forget what it's called). Granted they don't check very often, but if they do ask you for your ticket and you didn't stamp it, it's a big pain in the ass and an expensive fine. Transit tickets are so freakin' cheap it's not worth it to try to save them (in my opinion). A similar system exists in Austria but as far as I can tell, they're much more lax about checking the tickets. *shrug* And if possible, when arriving or departing Bratislava, try to NOT go to the Petrzalka train station. It's out in a suburb and kind of a pain to get to. I forget what the main one is called but it's right in the middle of town.
And don't miss Hrad Devin (Devin Castle, really just a ruin), a 20/30-minute bus ride from central Bratislava at the intersection of the Moravia and Danube rivers. It's wonderful! And free!
And be nice to elderly people taking public transpo-- give up your seat if it's a crowded bus/train/whatever.
Hell, try to do that anyway.