Not sure about abandoned bikes all over the place... I haven't seen any so far, just LOCAL abandoned bikes taken apart at bike racks
Bicycling in Hawaii is great. I commute to and from work in Honolulu by bike, and at times, it IS quicker than commuting by car!
As for rentals, there are many rentals all over Waikiki. Price, I do not know.
Only thing you have to remember is, NO bicycling on sidewalks anywhere in WAIKIKI and the main DOWNTOWN areas. That is the downtown business district off from Pier 8. Anywhere else, it is permissible, but with a 10 MPH speed limit.