Went on trip to Bratislava and Vienna earlier this year and stayed a few days in Bratislava and found it great. We stayed in the Hotel Danube right on the river overloooking the bridge with the viewing tower.
Hotel is good value and has two alright restaurants.
You are right by the Castle, and 5 minutes walk to the Opera house, Mc
Old city is small but cool, found a few great restaurants including one in hotel where we were lucky to be the only ones, being server by two waiters in full dress with tails and all. It is a place to relax and you can cover everthing in couple of days at your leisure.
Vienna is different since like Paris there is just so much to see.
You will notice difference in prices once you cross to Vienna. You can take train for less than €20 and arrive at the Subahnhof station in about an hour.
Note the border guards from both countries like to have a look at your passport as you get on the train in Bratislava.
Makes them feel important I guess.