+ good solid four-star hotel with well trained staff, all english-speaking.
+ nice breakfast
+ great spacious room with a huge bathroom (shower and bathtub), a Nespresso machine (free) and speedy internet (some people are complaining that it's too slow... Well, I can't doubt it, but in my case I was able to watch a live football translation stream, and it usually requires a fast connection).
+ asked the reception to arrange a taxi for us and got a very comfortable car (Mercedes) at the same price we paid at the train station (for an old Fiat).
+/- nice location just across the road from the old quarter. Actually, I wanted a hotel to be closer to the bridge and the castle, but it turned out that Falkensteiner is located much better. Although a few hundred meters away from the old town, it's in a more quiet location. Nevertheless, the farther you are from the touristic center, the dirtier are the surroundings. Bratislava itself is a soviet-era city with concrete grey buildings and nothing much to do. So I felt that this hotel is literally "on the edge" - if it was a step farther from the old town, the area would be totally depressing.
The last but not least. Some reviewers say that "you can find a cheaper option around" and suggest it to be Park Inn Danube. To be honest, I've also had that option in mind when choosing the accomodation. Finally, when in Bratislava, I was able to look at Park Inn at a close sight. Well, it's FAR worse than Falkensteiner, rooms more like 3* and the building is a concrete block without any charm. The only good thing would be the price (maybe?) and the proximity of UFO bridge, but that doesn't sound like a good deal.