Monica, I didn't mean to sound so welcoming. Welcome to ST.
Shannon is right. You will have a great time renting a place in Barça. The markets should really be listed as the wonders of the world. Once at a dinner, both Calvin Trillin and Alice Waters told me they thought the Boqueria market was their favorite in the world.
(I answered that they obvious hadn't been to Guangzhou's Qingping market, which I call a zoo with takeout...)
2 weeks ago when I was in Barça, I went to the new Santa Caterina market. It is faaabulous and very airy and much nearer my favorite neighborhood - El Born. But I did miss the euphoric chaos of the Boqueria, which is not that far away - about 15-20 min walk from El Born.
The rentals I have loved and swear by are:
http://www.bcngotic.com/If you are a family, choose the bigger surface apartments. Nearly all the apartments, big or small, have 3 bdrms. The smaller ones can be a little cramped. Owner Angel Font (French/Spanish/Catalan-speaking) is very responsible. The building is very well-run, with a manager (English-speaking) always on hand.
http://www.inside-bcn.com/The 1-bdrm apartments are perfect for a couple.
http://www.apartmentsapart.com/Europe/Spain/Barcelona/Apartments/Detail/25The latter 2 rentals - although located in the hipdom epicenter of the world - have a fatal structural flaw:
Some of the inside-bcn rentals are right above the chocolate shop Xocoa.
The last rental is on the same lovely little square as the legendary Cal Pep restaurant.
Rent them at your peril.
Bon voyage.