Test Drive Unlimited is/was open-road racing. The premise is that players develop their character's stable of cars (and houses to hold those cars) with money from various racing events, with the entirety of the Hawaiian island of O'ahu in the US graphically mapped out around which to drive.
Various set "challenges" (races) utilise portions of the game mega-map to outline courses (with the normal timed, head-to-head, group racing, elimination, etc. races) but the game also defaults to free-driving mode where the player can just navigate over the main map (and drive around the entire island) at their own leisure. In the online version, other players in the area can set up challenges with you where you define the start and end points of your race using the same over-map. In the offline version, there are AI-controlled cars that randomly drive around the area and drive near you which you can challenge in the same way for ad hoc racing (some with amazing halo/super-cars, and others with lower-tier cars also.)
The game is a bit old now, and the online servers are pretty empty, but it's a good offline game as well. There is even a "hardcore mode" where the game operates more like a sim than an arcade game, with much more realistic breaking and handling and acceleration dynamics.
Sometime in 2011 they will release
TDU2 so if you aren't still enamoured entirely with GT5 by then, maybe consider looking into that one. TDU2 will be set in Ibiza, ESP, so it will be another "island sandbox" type racer.