I think you've make a good choice by coming to BCN...
Don't worry about going to l'Eixample; actually it's not the best place to visit in BCN, despite having la Sagrada Família; it's just a residencial zone (in the European sense), in spite of hosting el Gaixample.
Actually you're staying relatively near to areas such as Ciutat Vella, Plaça Catalunya, el Raval, les Rambles, Passeig de Gràcia, el Born, etc. that have the most important places to visit, but some other places you can go easily by metro.
You're also near to the main and coolest discos' area; and obviously you've got el Gaixample pretty close... Anyway don't expect a common gay village like in other cities; it's much more integrated to el Eixample than others I've been told, but don't worry about meeting hot Spaniards, you'll find them almost everywhere.
If you need some more information just message me!
Have a nice stay!