Bob's Red Mill
has a ton of different flours. When they started being available in local stores here, I started experimenting with different types. The Bob's Red Mill site has a ton of recipes
for ideas. I've used white bean flour (very neutral taste), almond flour, WW pastry flour, etc. to make all kinds of things. It's getting easier nowadays to avoid white flour.
ETA: If you can't find these flours locally, they can be ordered online.