The obvious day trip from St. Thomas is to St. John, and it is genuinely excellent. Ferries run from Red Hook (20 minutes) and Charlotte Amalie (45 minutes) to Cruz Bay, the small town at St. John's western tip. Two-thirds of the island is Virgin Islands National Park, established in 1956 after Laurance Rockefeller donated much of the land to the federal government. The park contains some of the best beaches in the Caribbean — Trunk Bay, with its marked underwater snorkel trail, and Cinnamon Bay, longer and wilder — as well as hiking trails through dry tropical forest to Danish plantation ruins. St. John has far fewer cruise ships and a quieter character than St. Thomas.
The British Virgin Islands are accessible from Red Hook by ferry, though they require a passport and immigration entry. Tortola, the BVI capital, is the main destination; Peter Island and Virgin Gorda are more remote but rewarding. BVI day trips work well from St. Thomas, but factor in the border crossing time.
On St. Thomas itself, the drive east toward Red Hook and Sapphire Beach makes a good half-day outing, taking in the views from Compass Point and the calmer east-end bays. The Skyride to Paradise Point at sunset is a popular option for those who don't have their own transport to higher viewpoints.