Congrats on your new coach and welcome!
That hose should be a vent hose. I believe it connects to a fitting near where the fill tube goes outside. If there isn't something there, just make sure you have the hose up somewhere so that water doesn't go down through it if you fill the tank up full.
2007 T-286SR Cherry/Granola, #6236, original owner, current mileage: 9467.8 (as of 5/26/19)
1997 T-2653 Blue Denim, #5471
1979 12 1/2' MC, Beige & Avocado, #4639
Past Sunlines: '97 T-2653 #5089, '94 T-2251, '86 T-1550, '94 T-2363, '98 T-270SR