For me it definitely needs to have cars! Naturally you need transportation to travel in an open world game, right? So I enjoy those having automobiles.
Cars usually play a significant role of setting up the location and time period of the world too. For instance, you can see many boxy Japanese vans, but not a single American muscle car in Sleeping Dogs’ Hong Kong. Or that a specific type of vehicles can reflect its local car culture, like lowriders in GTA: San Andreas.
(Driving a 1st gen Corvette must be pretty stylish in the 50s, isn’t it? You can do that in Mafia II) 
Last but not least, I should add that I prefer driving myself to the destination rather than fast travel. It’s also where you get to enjoy the scenery and radio stations. And my “something not on this list” would include open-world racing games like Need for Speed series or Forza Horizon.