Hi Fontinini- it depends on the weather. The nicer it is the more people show. October is generally post-hurricane season in Rehoboth; however, so a good time to go if you don't mind not being able to swim (the water, I think, would be too cold), and not being able to sunbathe. Dolles and most of the boardwalk and Rehoboth Ave shops will still be open, but I believe FunLand is closed---or open only in the eves and on weekends only. The outlets are always open! But keep in mind they're not really outlets--they're just stores made to look like outlets, and I've only ever found the QVC outlet, the seasonal stores, and candy outlets have truly discounted prices over what I'd pay at home for the same.
As for lodging...I read the other poster's comments, and you CAN actually find some cottages for rent. You have to call the agencies who rent them tho. Go to Jack Lingo or Long & Foster's websites and ask to speak with an agent about off-season rentals. You would be renting by the day, not the week, I assume. There's also a number of hotels right on the Boardwalk and a block back that offer cut rates during the off-season. There's a plethora of inns both in Rehoboth, Bethany Beach (20 minute drive to RB), the town of Lewes (15 minute drive to RB), and historic Cape May; an hour by ferry across the Delaware. You can take your car across, or go on foot.
Look at homeaway.com to connect directly with a home owner with a property to rent. A lot of their stock shows houses to rent during the off-season by the day or week. Good luck!