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: