The City of Gainesville's website has a page dedicated solely to recycling at:
It also includes a link to an A-Z Source guide where you can look up almost any item that can be recycled (including Electronics). The guide will also give you detailed information on where you can donate them or take them for recycling. If you prefer, feel free to call the City's Solid Wast Department at 352-334-2330 and they can help you.
City of Gainesville
City Manager's Office
The Arc of Alachua County has an e-recycle program, they are located near Santa Fe College off of 39th Ave. Their number is 352-334-4060.