After spending a while wandering around town trying to find a good cocktail bar, my girlfriend and I stumbled upon Boutiq Bar. The drinks menu was extensive with influences coming from all around the world. The bar also had a fantastic list of spirits so anything not on the menu could be made at your request. Price wise, it wasn't cheap by Budapest's standards but it's safe to say that it wasn't terrible expensive with prices generally falling into the same bracket as most standard cocktail bars in the UK (£4 to £6 for a cocktail). However, the quality of the cocktails provided is much greater than any bar I've been to in the UK, the volume of alcohol is high and the attention to detail is even greater so everyone's happy!
The bar staff were friendly and were happy to offer you advise on what to do in Budapest. If you're in the area and have some spare time then I'd definitely recommend visiting Boutiq Bar as you'll never go to a cocktail bar this good anywhere else.