Can you recommend any places to stay, besides the campground?

There are a few Bed & Breakfast inns in the area.  The one I recommend is Casa Escondida.

Casa Escondida is an authentic adobe, 8-room bed & breakfast that is located in historic Chimayo (only 35 - 40 minutes from Pilar). They offer a rural, secluded setting with great mountain views. A full, hot breakfast is included. Enjoy their relaxing outdoor hot tub after a long day of paddling. Rooms range from $99 - $159 / night. FREE Wi-Fi. Pet-friendly. Book online or by phone: www.casaescondida.com / 505-351-4805