Brno and Vienna are indeed good choices. Budapest is also doable, although it takes a bit more time. You can also take a look at Gyor (mind you, it takes two transfers and you would probably travel by regional trains). Other destinations in Slovakia such as Trencin or Banska Bystrica can be also worth taking look at.
Other destinations depend on how much time are you willing to spend on travelling. I used to do Prague and Kosice as a day trips, but it means leaving Bratislava at 6 and coming back at 22 (giving you something like 7-8 hours in the destination).