There are 2 really good outlet malls-they do have covered outdoor walkways-here's a quote from a site:
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Across the bridge on the mainland, Hilton Head Factory Stores 1 & 2 comprise the largest outlet center in the area. The two sections with a total of more than 100 outlets are within a mile of each other just minutes from Hilton Head. (The Cross Island Parkway makes it about a 10-minute ride from Sea Pines Circle.)
Brand names include Bass, Black & Decker, Brooks Brothers, Bugle Boy, Danskin, Eddie Bauer, Etienne Aigner, Famous Brands Housewares, GAP Outlet, Geoffrey Beane, Harry & David, Jockey, Kitchen Collection, Lauren by Ralph Lauren, Leather Loft, Lillian Vernon Catalog Outlet, London Fog, Royal Doulton, S&K Menswear, Van Heusen, and Waterford/Wedgwood, to name some of them.
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Last time we were there it rained one day, we did the behind the ears tour in the rain, and then after we went to Barnes & Noble and browsed around in their for quite awhile, got the kids a movie when we got back and they watched that while we lounged around.