Does your friend like museums? Art? I recommend The National Gallery at Trafalgar Square and The Wallace Collection near Oxford Circus. The Wallace is smaller but contains several old masters. If your friend is looking for a museum that has a little bit of everything (textiles, art, sculpture, costume), my favorite is the V&A in South Kensington. Also in South Kensington is the Natural History Museum and the Science Museum if your friend had those interests.
Another one I like is the Sir John Soane museum near the Holborn tube station. It’s a small but interesting collection of antiques, paintings, and sculptures.
I don’t know how much time your friend has in London but if they have limited time and want to visit the British Museum, I recommend they plan in advance which areas/collections they want to prioritize. (They can check out the collections online.) Wandering around that place with no plan to is too overwhelming.
This is nerdy, but I loved it: Parliament tour. They’re available on Saturdays and sell out quickly. Seeing what remains of the Palace of Westminster was worth the price of admission for me.
Depending on your friend’s interests, there’s the Churchill War Rooms which are interesting and the Tower of London which is popular so be ready for crowds. If your friend goes to Westminster Abbey, I encourage them to pay for the additional ticket (and it’s a timed ticket due to limited space) to see the Galleries. There are a lot of cool medieval treasures on display up there. Another of my favorite places to visit is the Ritblat gallery in the British Library which has a huge assortment of treasures on display from ancient to modern.
I’m assuming your friend knows this but they should look at the Transport for London website to get familiar with the contactless pay options for the tube and buses. The tube is fairly straightforward, color-coded, etc. and works the same as most metros in other cities.