I'm not sure exactly how things work, Hebei, but I imagine they are pretty similar to where I am. Beijing though, I don't know the ins and outs.

Hebei plates will be cheap to insure and cheap to buy on a 2nd hand bike. You could almost leave the plates from the previous owner on there and pop down to insure the bike each year without changing the name over, saving a bunch of hassles. I recently bought insurance on my bike, even though it is registered in my wife's name they didn't ask to see her ID card. On the downside you'll have far less choice and the probability that the cops in Beijing will hate to see your out of town plates if you try to ride into town.

Beijing I think will be more expensive and more hassle, as you'll probably be forced to change the documents.

Hope someone chimes in with more knowledge. Best of luck.

Jackson Hole? Are you a skier or snowboarder?