I've been waiting on that one until I get a PS4, since from what I understand the XB360 version never got the updates that substantially improved the game. I was also turned off by the strong online emphasis and I was doubtful the physics would be up to par for me, but if I can play the game by myself, I'm sure a used copy would be worth it.
Fair enough, nah the 360 version would be a long way behind the current gen versions. As for your other concerns, I bought the game second hand a long time ago, without really knowing much about it, because I had only just got my PS4, and wanted a bunch of different games to have some variety, and when I found out it had so much online capability, I was concerned about it affecting the offline game, especially as I didn't plan to get a PS+ subscription. However, the offline story mode, despite having a story almost as lame as the average NFS game, is quite varied and takes a bit to complete, and the online stuff doesn't impact the offline game's playability. Even without PS+, you're still placed on the map with other players, and allowed to drive around with them, you just can't enter head to head races and crew events without PS+, but to be honest, I never got into that, even once I had PS+.
The map is simply enormous for an open world racer, and has a ridiculous amount of variation within it. There are tons of events and things like that, separate from the story mode, found all over the map, and some are a lot of fun. Around the map you'll go from big cities, some individual cities in the game are as big if not bigger than the entire NFS 2015 map, to countryside with awesome dirt rally roads, to desert with big dunes, to alpine regions with snow capped mountains, to swamp land. You'll find a bunch of racing circuits, including Sebring and Laguna Seca, and you'll find miniature versions of both Pikes Peak and the Bonneville salt flats. All of that doesn't even scratch the surface of the variety the game has to offer, Especially if you get the Wild Run expansion. At the price it's currently selling for, it's ridiculously good value.
As for the physics, I'd rate them as very good if not excellent arcade physics. Not as good as Driveclub, but a million times better than NFS. Also, The Crew is compatible with all PS4 compatible wheels, including Fanatec wheels, since it's an older game, and it drives surprisingly well with a wheel, which also shows the competency of the physics.