Denise, note that renting a bike is a great way to visit the city... but, not necessarily the best, much less for "the whole time you're here". Firstly to mention that riding on the sidewalk is forbidden -despite you'll see some riders still doing it- and subject to fines. Riding on the pavement can be sometimes a bit dangerous because although having lots of bike lanes, not all streets do and mingling with traffic is always a risk. Also note that you can't simply "park" anywhere you please, only in the spaces for bikes: http://bit.ly/1y3Najk -sorry page not available in English, use Google Translate, but you can see the pics also the PDF on the right column shows the parking spaces for bikes across the city. Note that this: http://bit.ly/1TcARNi is not allowed and bikes can be removed by the City Hall.
On top of this, Barcelona is really a city made for walking because, despite its size, you always have something interesting to do/see at a "10 minutes walk" from wherever you might be in the city. And when you need to move to a different district or crossing the city then public transportation is fast, safe, clean, efficient and cheap: bus/metro/tramway.
So.... if I were you I'd plan to rent a bike "for a day" instead. Also to mention there's a bunch of other equally fun manners to enjoy riding a day in the city, such as:
Segway...www.segwaytours.cat | www.barcelonasegwayfun.com | www.segwaystp.cat | www.segwaytours.cat
Classic sidecar... www.ridebrightside.com
Scotter... www.via-vespa.com | www.tumotorent.com | www.barcelona-moto-rent.com
Helicopter... www.barcelonahelicopters.com | www.cathelicopters.com
Go-car... www.gocartours.com
Rickshaw... www.trixi.com
Lastly to mention, just in case anyone wonders, the City Hall bike service www.bicing.cat is only for residents of the city, sorry.