MKE dining near Bradley Center
Not sure which bars you already go to...
If you want to stay very close/west of the river, we have had some good apps/sandwiches at Tutto.
There is also a newer sports bar called Upper 90 that is supposed to be better than average for food. We have had beers there only, but saw some good looking bar food being served around us.
While you will likely not be wowed by the food, they do have a great happy hour (drinks and food specials) at Molly Cools. They even run it on Saturdays, so that's a bonus.
The Cheese Bar is also a nice calm destination for snacks and drinks.