As well as the Science Museum, the Wellcome Collection is brilliant for science meets art. It's much smaller and more manageable too. It has a permanent exhibition on Being Human, and two temporary exhibitions on Joy and Tranquility. It's free, and we just turned up.
Nearby is the Grant Museum which is a Victorian comparative anatomy museum, small but fascinating - that's also free but booking required.
Brunel Museum and Old Operating Theatre might also appeal to his scientific mind, alongside Greenwich Observatory as suggested.
Food wise I'd suggest a food hall or market as you can browse and choose things from all over the world. Mercato Metropolitano is amazing but often has long queues at the Elephant and Castle one, there is one in Mayfair too. Also look at Borough Market, Box Park and Camden Market. Princi in Soho offers a variety of food too, more of a cafe and really nice interior.
For seeing the sights, walking is cheapest, a bus is second cheapest - route 15 and 11 are often recommended. Then bus or river tour. I'd suggest making a list of what are must sees, and grouping things together by area so you're not dashing all around London.
Anyway I blog about London for families and have an 18 year old so happy to offer further advice if you like. I'm on IG instagram.com/museummum or blog at museummum.com