Stayed in Santa Fe last year, then rode the San Juan Skyway.
Stayed at Double Tree, across from Sante Fe Harley. Has a nice Brewery behind it.
Rode 3 days, no issues with the truck and trailer staying there.

 

It doesn't really matter where you park the trailer, just as long as no one can see it in the pictures you take of you, your bike, and the various landmarks you "rode to".

 

You may also check with the Dealerships if their is one in the area you are traveling. Never left one there myself but know a couple of folks who have at several locations around the country. If it is a dealership with a large enough parking area it may be worth a phone call

 

I had ask the dealer in Santa Fe if I could park the trailer there, if the hotel had issues. They said no problem.. But the hotel had no issues so... worked out good.

 

One thing I've done in the past when trailer parking was an issue was to rent a uhaul trailer. Turn it in to a local uhaul dealer upon arrival. Then rent another trailer for the trip back.

 

I've left a truck and trailer in a Uhaul Storage facility for a week while out.
Charged me $40/wk. secure and had cameras.

 

Just ride up...

 

Friends of ours call around to local HD dealers where they travel too and inquire about leaving vehicles in their parking lot. Usually works out for them. If not, the dealer would more than likely point you in the right direction as Id think it would be a common question. Another option is a campground.

 

I leave my trailer at any KOA campground. It will cost you 5 to 10 bucks a day but very secure parking. KOA's are everwhere.

 

Call ahead, not all of them will let you. Especially when they're busy.