The Thames flows through London from East to West. Many famous destinations are along the river, and even on the Thames, you can get to see many exciting places, like the Old Royal Naval College (e.g. in Thor: The Dark World) as well as the Tower Bridge.
Many boats and ships travel along the Thames for numerous reasons. One interesting option is the Thames Clipper, which is part of London’s public transport network, and you can travel on it using an Oyster card. The clippers travel from London Eye to Woolwich in the east, and on the way, you can see many landmarks like the Tower of London, The Shard, London Bridge, Tower Bridge, Greenwich and the O2.
Thames Clipper is definitely worth the experience for only £7 from one end to the other. You can also get a day pass, where you can get off whenever you want and hop on as many times as you like. Tickets are £18 for adults and about £16 for a family ticket. You can find detailed price information at https://booking.thamesclippers.com/river-roamer.html.
Another option is a river cruise, where you can also enjoy food, drink and music along with the sights along the river. You can get an exhilarating experience too, like with the Thamesjet speedboats for a 50-minute trip, which can start at the Westminster Pier, for example (note: minimum height 1.35m).