You could try iRacing -
http://www.iracing.com/all-star/
I don't know if it's totally free from cheaters, but they take the whole thing pretty seriously, keeping lots of statistics and running official race series.
If you're fast enough to set world records with GTR you'll probably do well with iRacing, and if you get into the top tiers of that you'll be mixing it up with real life professional car racers, which could be interesting.
iRacing is pay to play, but it's not that expensive to start off. Check it out if you want to see where your lap times rank compared to some of the best real and virtual racers in the world.
I don't use the iRacing service myself, but I think it's worth a look if you're into that sort of thing (competitive car-racing simulations).