Hm... When you say ALL of the NFS series - I assume you mean "Need For Speed: World" (http://free.origin.com/racing/need-for-speed-world)
as well... So I'm trying to think of what could work for you.
Most racing games don't offer a free roam mode sadly.
A game I was playing recently (DIRT: Showdown) (Looks like this: http://www.youtube.com/watch?v=d_q9R9sGxyE
) offered a mode where you could drive around freely (in an arena type of match - ramps, things to drift through, etc) to test out new car modifications... They also have a destruction derby mode, etc.
As a response to your mention of Grand Theft Auto: Have you tried "Saints Row The Third"? It was on sale for $12 a few weeks ago in a STEAM sale. ( http://www.youtube.com/watch?v=7x5qsLDnOo8
) It was pretty fun for a few playthroughs... Then it got old for me :P