Let'er get wet, ike.
As others have stated, utilize the overhang at the hotel/motel (most establishments will let you if you keep it out of the pedistrian traffic areas).
IMO, never thought a cover was a great idea anyway. You've just riden 300 to 600 miles and have all sorts of "stuff" on the front of the scooter...hey, now lets put a cover on it!
And yes, before the naysayers and pro cover folks chime in, I do attempt to clean on the bike a bit (more the windshield these days) before bedding her down for the night. Dew, fog, damp night air (or rain...) will settle on it overnight to make it all dirty again so why clean it at night to have it to do again in the mornig. So I have moved my, as 2K stated "whores bath" for the morning ritual so Ginger will be ready to get dirty all over again....plus the overnight dew/moisture helps with the cleaning process.
In my travelling style, putting a cover on a wet/dirty bike smearing the bugs/gunk all over the bike and inside of the cover and then having a dirty, wet cover to pack the next day.....and do it all over again at the end of the next day....dat jus don make no sense 2 me