There are multiple condo's available for daily rentals in the area as well as the hotels listed. Although they may require earlier reservations. They are easily searched for online.
Hotel
Fenwick Inn
1200 Coastal Highway Fenwick Island, DE 19944 (302) 581-0046
DOG FRIENDLY, GOOD PRICES
Hotel
Holiday Inn Express Bethany Beach, an IHG Hotel
39642 Jefferson Bridge Road Bethany Beach, DE 19930 (302) 541-9200