Here are a couple places that you can book to stay that are near Palmer. There are more places to choose from in Anchorage, but there is about a hour drive.
Hotel
Grand View Inn & Suites
2900 East Parks Highway Wasilla, AK 99654 (907) 352-1700
Hotel
Microtel Inn & Suites by Wyndham Eagle River/Anchorage Are
13049 Old Glenn Highway Anchorage, AK 99577 (907) 622-6000
Travel Note
Air BnB
We have had good experiences with Air BnB, there are a variety of places on this website to chose from.