Juniper in the foothills. CUT ONLY WHERE LEGAL. Juniper trees can approach 1000 years old. Look for a big tree with spreading branches and cut a stave from the top side of a long shaded limb at the base of the tree.
mountain mahogany is AMAZING bow wood, if you can find a stave of it. I have it all over Uah, but it is scrubby. The only satves I found were in large thickets of tall trees in a wash/canyon in the extreme NW corner of Utah.
If you have to forage in town, look for vacant lots, river bottoms, along roads, and ditchbanks. Elm, plum, locust, ash, and various other domestic-gone-volunter trees will grow there.
Your mountain foothills and mid-elevations should have canyon maple, juniper, oak scrub and the like.
If all else fails, find a couple of ash shovel handles, with growth rings the whole length, or nearly, cut off the tapered part where the shovel head goes, chase a ring, and splice at the handle.