I've down a trip bikepacking/hiking in Utah, Arizona and Nevada. Most days I would use a campsite as basecamp to go hiking and keep my bags inside the tent, then either lock the bike there or lock it at the trailhead. At the hikes where I had my entire set up with me I've asked ranger stations and even restaurants before if I can secure my bike somewhere. Never got turned down.

I've left my loaded bike inside supermarkets before as well when I needed to go shopping. Asking nicely generally gets you a long way.