Tate, National Gallery or Barbican. Check to see which has the most interesting exhibitions while you are there.

I enjoyed the V&A and the Tate, but the Natural History museum is fabulous if science is your thing.

Of your suggestions, V and A, but...

My own kid's preference at that age was the National Portrait Gallery. It's history, yes, but often the most interesting part of history for non-history buffs is what people looked like.

Tate modern.

Agree V&A in this case

I haven’t been in years but really liked the London Museum—it focuses on the history of the city of London.

V&A is great. My kids liked the Churchill war rooms. My favorite as a teen girl in London was the National Gallery. Just the grandeur and quiet of it, and the location on Trafalgar Square.

I loved the Churchill War Rooms AND the Imperial War Museum - real replica of trench warfare you can walk through.

V&A for sure. Lots there, and the Cartier exhibit is supposed to be good.

I am also a fan of the Tate Modern, including the restaurant on the top floor. It's more about the building than the exhibits themselves.

V&A or the Wallace Collection

The V&A, especially if they are interested in clothes or do any type of arts and crafts themselves.

V&A

Tate Modern.
Personally I thought the Churchill War rooms were only ok. The rooms were cool enough but the museum dragged on. And it’s very crowded.

Banksy

What is your vote with 2 teen girls (not particular history buffs, but not totally disinterested either.)

Options:
1. Victoria and Albert
2. Churchill War Rooms
3. Natural History (I'm least inclined to do this one I think)
4. Nothing, 1 museum is plenty!
5. Other