Theres a bunch of bars outside the stadium, and they are extremely safe. I usually park at a deck and tailgate, a lot cheaper and a better beer selection.
THIS. If you are going to the game, you want to drink near the stadium. There are a lot of bars right outside the Stadium on River Ave (underneathe the elevated subway tracks)and they are perfectly safe on game day. There is also a Hard Rock Cafe where you can drink outside and it's connected to the Stadium.
Of course, you don't really want to hang out there too long after the game or on non game days.
I literally live 5 miles from the Stadium, but will only be showing up with Detroit comes back to town.