It took me close to 800 or so but it shouldn't take you that many. Just use the same set of tires for all your games (which helps)and you'll eventually get it. Now that online matches count it should come a lot quicker for you; I had the 250km notification on ~Friday and the 500km trophy on ~Monday (days are made up but spread is accurate).

The NA PSN Store updated with new sales themed on Capcom's and Square Enix's titles :D. 

For the Capcom Sale, the following games are on sale:
-DmC: Devil May Cry PS3: 11.99
-DmC: Definitive Edition (PS4): 23.99
-DmC Ultimate Editions (PS3; all DLC included): 16.99
-DmC: Vergils Downfall (PS3; extra story mode with playable Vergil): 4.49
-DMC4 Special Edition (PS4): 18.99
-DMC HD Collection (PS3): 9.99

For the Square Enix sale, the following games are on sale:
-FFIV: The Complete Collection (PSP/Vita): 9.99
-Tactics Ogre: Let Us Cling Together (PSP/Vita): 9.99
-Final Fantasy VII/VIII/IX (PS3/PSP/Vita): 4.99 - PS TV
-Chrono Trigger/Chrono Cross (PS3/PSP/Vita): 4.99 - PS TV
-Dissidia Final Fantasy (PSP/Vita): 9.99 - PS TV
-Final Fantasy Tactics: The War of the Lions (PSP/Vita): 4.99 - PS TV
-Final Fantasy III (PSP/Vita): 9.99 - PS TV
-Final Fantasy XIII-2 (PS3): 9.99
-Final Fantasy VI (PS3/PSP/Vita): 4.99 - PS TV
-Final Fantasy Origins (FFI and FFII; PS3/PSP/Vita): 4.99 - PS TV
-Final Fantasy V (PS3/PSP/Vita): 4.99 - PS TV
-Legend of Mana (PS3/PSP/PS Vita): 2.99
-Legacy of Kain: Blood Omen (PS3/PSP; Not PS3->Vita Transferable): 5.99
-Front Mission 3 (PS3/PSP/Vita): 2.99 - PS TV
-Lord of Arcana (PSP/Vita): 9.99 
-The 3rd Birthday (PSP/Vita): 9.99
-Drakengard 3 (PS3): 19.99
-Crystal Defenders PS3/PSP: 4.99 per version
-Dissidia 012 Final Fantasy (PSP/Vita): 19.99 - PS TV
-Elevator Action Deluxe (PS3): 4.99
-Final Fantasy X/X-2 HD Remaster (PS3): 14.99
-Xenogears (PS3/PSP/PS Vita): 9.99
-Final Fantasy Tactics (PS3/PSP/PS Vita): 4.99
-Vagrant Story (PS3/PSP/PS Vita): 2.99
-Threads of Fate (PS3/PSP/PS Vita): 5.99
-Lighting Returns: Final Fantasy XIII (PS3): 14.99
-Moon Diver (PS3): 7.49
-Parasite Eve I and II (PS3/PSP/PS Vita): 2.99 (PE1 isn't on the PSN Store for some reason; no link to buy the game. Should be on soon though)
-Thexder Neo PS3/PSP: 4.99 per version

Hope this helps and that you guys lots of Square/Capcom games :D! Lots of good stuff on sale in the Square sale :D.

Edit: Will state a few things that this didn't clarify.
-DmC PS4 is a dramatic improvement of the original PS3 game (60FPS, tighter combat mechanics, turbo mode that matches the feel of past DMC games, improved visuals, Virgil DLC, ect), so its well worth its sale price.
-Various games listed for the sale aren't at a sale price yet. I will update the OP with the new prices once the PSN store fully updates (will check back the PSN store by 5-6PM to be safe). Once the prices are update, will edit the OP with the new prices :). 
-Parasite Eve 1 isn't listed as buy-able for some reason. Will update the OP with a link to the game once PSN fixes that

Holy shit that was more than I was expecting. Only done 170, almost all online, so those may not even have counted.

TBH the majority of those games were played before the patch that allowed online driving distance to be counted. After that patch I got the trophy quite quickly

Rocket League update 1.04, which includes the new Arena called Utopia Colosseum, Spectator Mode and cross-platform Private Matches is out now!

Any decent person should log in here and upvote this idea:
http://share.blog.us.playstation.com/ideas/2014/05/20/ability-to-change-gamer-id-update/

More downvotes than ups. :/

Are we looking at the same idea?

I'm kinda on the fence with it. 

It's at 27,586 up and 31,603 down.