You can walk around the USA and find flint arrowheads ... not sure the Native Americans used coins as such.
Yeah the wild thing about the southwest is the open-air museum aspect of it, not the layers on layers. For petroglyphs, the southwest has so many that date to the high middles ages (~1100 AD) you can stumble on them by accident as a hiker. AFAIK the oldest in the area are still thought to be these ones[0], about 9000 years ago. (Always controversial to date rocks I guess, but the oldest North American mummy should be easier and is about the same.[1])
[0] https://en.wikipedia.org/wiki/Winnemucca_Lake [1] https://en.wikipedia.org/wiki/Spirit_Cave_mummy#Dating
Growing up as a kid, we used to find old wagon wheels and arrow heads frequently. There used to be an old fort not far from where my parent's house was located. A limestone creek ran on the back part of their property and defined the property line. We'd find all sorts of artifacts up and down this creek. I even came across a rock with an circular hole that was obviously bored into it and charring around the hole. I used to have some interesting show-n-tells. This was in the 80s.
Old trade beads can sometimes be found, old stashes and caches. Pony beads, seed beads, and others. They were traded/used as "money". The Hudson's Bay Company brought millions of them to this continent.
I grew up in the bed of a drained lake (https://en.wikipedia.org/wiki/Chicago_Portage#:~:text=this%2...), so there were no native American artifacts to be found. The best we could do were the foundations of some homes that had been on sanitary district land but then torn down with the area reverting to forest (sadly, this forested area which was open to exploration when I was a kid has since been fenced off).