I can't go to a museum without meandering through the gift shop, especially this time of year with all the seasonal goodies. Many museums shops sell crafts, decorative items, foods, stationery, toys, and books. These are great places to find a special gift, and make a purchase supporting local cultural institutions.
The best way to enjoy shopping is to visit the museum, then make a personal appearance in the store, but some museums have online catalogs for your convenience. I'm listing a few links here, but I haven't personally tested these museums' online services.
Morikami Museum and Japanese Gardens Store
Flagler Museum Store
Henry B. Plant Museum
Florida's History Shop
Edison & Ford Winter Estates Online Store
John and Mable Ringling Museum Store
Key West Art & Historical Society Online Store