Green Chile Pork
(you can use other cuts as well, pork shoulder works fine!)
Otherwise, I buy cheap beer frequently to brine various chicken dishes. Sure, it’s not a lot more flavor than water, but more is more. 
A light-tasting beer batter for fried food would also work well, or even in a tempura batter.
Lastly, I often sub out some chicken broth (not stock, broth) in stewed dishes and soups with various lower flavor beers. Or use it for a braising liquid in any dish that would call for a mild white wine.