This is my small blogspot with a few curiosities:
http://gironaguide.blogspot.com.es/

A shop with bikes, 5 minutes from the apartment:

http://www.gironacyclecentre.com/

A friend of mine is a professional guide and organizes hikes in the nature:
http://aventuragirona.com/en/

Also, you may try an alternative way to rent a car:

http://www.socialcar.com/alquilar-vehiculo/girona