Well, you get 5 choices currently if you decide to play on PS4. There are Rivals, NFS 2015, Payback, Heat, and Hot Pursuit Remastered. Good news is all of them have free-roam mode you ask for. Although I WON’T recommend Rivals and 2015 for the following reasons:
Rivals is a ‘busy’ game, at least that’s from how I view it. The game automatically connects you to a multiplayer session. You will have to leave the session later in order to start your personal session. That’s not very peaceful. Plus, if you play as a racer, you will always be chased as soon as an AI cop sees you, even if you’re not moving at all. So in the end, you probably won’t have too much time to appreciate the game’s sceneries.
2015 is an online-only game, which means it suffers from what Rivals did too, except it won’t even allow you to play offline. The game’s physic and handling can be somehow whacky, your car can become very unstable when getting into high speed. The game also only sets in an always nighttime urban environment, so don’t expect to see sunrise and go for a Sunday drive.
The remaining 3 games, Payback, Heat, and HP Remastered should suit your need well when it comes to freely explore the world. Although HP Remastered doesn’t quite tick the optional customization requirement you list. It only allows you to change color and edit wrap. The other two should provide you sufficient amount of custom options.
Well that’s all, thank you for reading this. I hope you find this post informative.