I went to Amsterdam for four days last summer and I spend most of my time in bars or clubs. There is a lot of bars and clubs around a place named Rembrandtplein. One of the club there was quite expensive so you should check with the locals to know if there is events and what kind of place you’ll enjoy depending on your interests. Amsterdam is definitively a party city. I also went to club Paradiso near Leideseplein place which is actually a club in a old church. I know I prefered the clubs around Rembrendtplein more than the Paradiso, maybe because of the music. Hiope I helped you there.

I forgot…
I was 19 when I went to Amsterdam and nobody nerver asked me for an ID.
In 4 days, I went to 3 different clubs, 10 different bars and ID wasn’t required to order alcohol or enter. I’ve seen a lot of people looking like having no more than 16 years old in these places. In coffeeshops, if you want to buy something, they might ask you a proof of your age (must be 18 for soft drugs).
For Bratislava, I don’t know. I’m going to Prague this summer and would be interested if anyone knows good place to go out. Don’t hesitate to descibe fully the atmosphere of these places.