Royal Hospital Chelsea is the 17th-century home of the Chelsea Pensioners, founded by Charles II and designed by Christopher Wren. The grounds, chapel, Great Hall, and museum make it a substantial historic stop rather than just a handsome institutional facade.
Tours are the best way to understand the site, since the hospital is still a living community. If you are already visiting the Chelsea Physic Garden, Battersea riverside, or the museums of South Kensington, it fits neatly into the same part of London.