I was just there 2 weeks ago and stayed at Equity Centric: http://www.equity-point.com/en/hostels-barcelona/centricpoint/general-information.html
I thought it was nicely located in the middle.. from what I understand the gay area is about a 10 minute walk west of there, but not 100% if that's where the clubs are (honestly, my only experience was walking down there one evening and it seemed quite dead.. from what I understand nightlife only starts way past midnight)
The metro station is 2 minutes from the hostel, and you can use that to go to the beach (or it's about a 40 min walk).. get a T10 travel card, it makes things a lot easier.
The hostel itself isn't too bad.. the staff were friendly.. people can get a bit loud at night, and could do with more thorough cleaning. But for the price, it was fine.
That chain has a few hostels in Barcelona, one is closer to the beach.