There is BLM land all around to ride.
Pio Pico (and similar Thousand Trails resorts) have hiking trails within their campgrounds but not off road. You'll need to leave the campground gates for that. I don't think the campground allows off road vehicles on their roads either so if you have a vehicle that isn't street legal you'll need to tow it through the gates first before using it.
I saw some offroading right near it...but not sure if it is part of pio pico.
Yes right at the camp ground
Yes, I believe there is some areas nearby the skydiving site
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