I'll just say it. You can't go wrong with Hradná Hviezda.
Whether you're a tourist looking for the best restaurant in Bratislava, a business owner on his work trip or a family looking for somewhere nice to eat, combine a visit to Bratislava Castle with a visit to Hradná Hviezda.
Hradná Hviezda specializes on Slovak cuisine, so don't expect caviar and seashells here. You should rather be prepared for many types of meat (their steaks are especially awesome), mushrooms and typical local specialties like the famous bryndzové halušky - basically dumplings with a special type of sheep-cheese and bacon. You should definitely try them.
I am a regular here and I've befriended the owner after a few visits. He is one of the most intelligent, honest and hard-working businessmen in the food industry I've ever known and it shows on the level of service and food quality. He also employs one of the best Slovak chefs, which means you don't have to worry about the food not being of top notch quality, unlike some other Bratislava restaurants.
They offer a wide selection of Slovak wines of similar quality as the food is - only the best. I presume you don't know much about Slovak wines, but don't worry, you'll like anything they recommend.
The prices aren't the cheapest in the world, but compared to other restaurants in Bratislava of this level you won't go broke. The prices are well set and you pay for the quality presented, nothing more, nothing less. Add a service fee of 10% and there you go!
The restaurant is located directly in the Bratislava Castle courtyard, which is a blessing of heroic proportions - because you can kill two birds with one stone. Plan a trip up to the castle, enjoy the view and refresh yourself in Hradná Hviezda, it's that easy.
The service understands English and German, they have menus in English, German, French and Russian.
Closing words? If you are ever in Bratislava, visit Hradná Hviezda. It's easily one of the best restaurants in Bratislava.