Shopping malls, restaurants and cafes offer free wi-fi
Some of the hostels have free wifi too, see http://poorbuthappy.com/colombia/travel/place/bogota/
The chain of Bogota Beer Company pubs, Archie's pizza places, and Juan Valdez cafes have closed but free wifi. Each store has its own local network (and hence own password), but the staff always provide the password when asked.
Most restaurants and cafés have free wi-fi connection. Just ask restaurant personnel if the place is not already marked with the wi-fi logo.
The Hotel El Campín, has a free WiFI connection, its a Hotel three star certificate for Cotecna A Swiss Group, you can find more information in this page http://www.hotelelcampin.com