Mountain mahogany should make some fantastic bows, but I tried and failed on the couple very marginal pieces I played with. It's really scrubby, branches a ton, and had crooks and knots everywhere.
Up in the top north-east corner of Utah in a place called One Mile Canyon in the Sawtooth Mountains, where I used to hunt deer with a bow, I once saw a huge gully/canyon full of LARGE, tall mahoganies packed into a shaded low-lying area. Many had been pushed down by snow and they were the biggest straightest trees I've ever seen anywhere of the species. I have meant ever since to go find some staves up there, but I always have enough wood, little time, I hunt somewhere else now, and it's a three hour drive each way....... one of these days, I guess.
I wouldn't harvest much of anything off the open foothills on the Wasatch Front, but up the canyons there should be plenty of maple. The Bountiful Peak loop has you driving by tons of it. I confess I didn't get a permit, but I was in a wild back area and took one small tree from the middle of huge mile wide thickets of the stuff, and I've only done that a couple times. They cut tons of it down as they clear lots for houses, along with the oakbrush. Sometimes when working on trees for money in the houses invading the foothills I get the maple. So far that's all I have needed or used.