Need Duel in the D advice for this weekend

My wife and I are driving up to Michigan from Virginia this weekend to spend some time with family and take in the UM/MSU hockey game at LCA on Saturday. She doesn't care much about sports (though all things Michigan are rubbing off on her), but one of our first dates was a (non-Michigan) college hockey game and so she bought us tickets for Christmas.

However, it's been at least 10 years since I've been downtown Detroit, and that as a teenager so my experience there is lacking. We're staying with my sister in GR Friday night and heading over to Detroit sometime on Saturday. I got a hotel over in Romulus since that's on our way home anyway.

But I don't really know what's good to do in the area around LCA for the time that we're there. Specifically, where is good to go for dinner that's reasonably priced? I'd love to take her to a good coney place or get some Detroit pizza, but I grew up in Flint, not Detroit, so I have no idea what I'm doing.

Also, is there anything in the area that we should not miss out on? Anything in LCA we ought to see? I'm already planning on taking her by Comerica/Ford field and maybe down by the Joe, just so she can see them.

As far as the game goes, this will be her first Michigan sporting event and my first Michigan hockey game. Especially for a neutral site game like this, what should we expect? I have no idea how rowdy students are nowadays or if many students will even be there. Would love to show her a good crowd but LCA isn't Yost. I'm also not sure how chants and all that go but I'm sure we'll pick up on some of that as the game goes on.

Of course, I'm doing my own research as much as I can, but I trust mgoposters way more than I do the rest of the internet. Thanks for any information you can give us. Go Blue!