A lot of hotels and tent stay are situated near Kedarnath.
Tent stay list
R K Adventure Camp Stay
Mount Kedar Tent
Nandi Complex Base Camp
Kedar camp resorts Mount Holiday Chhani Camp, Kedarnath
New Himachal House Rajasthan Bhawan
New Krishna Lodge.
If you want to stay free then you can register couchsurfing.com and search your destination. Then message or call to your chosen host. if they want to keep you in their house, you can stay there freely for 1 to 3 days.