San Francisco is one of my all-time favorite destinations with a GT kiddo, but Paris or London is also an amazing and rich environment.
Why is SF one of your all time favorite locations? It's one we get to quite often because grandparents live nearby. Took DS to the Explorotorium last fall, and we like the new Science Museum. And I enjoy several of their art museums. We tend to drive through SF a lot, and see it one day at a time. Is there something special you like there?
We did London when my son was in Elementary. Would love to do Paris, but it's out of our budget right now.
Museums galore-- and culturally distinct/diverse neighborhoods, Alcatraz, MBA, Marin Headlands, etc. etc. Muir Woods-- all day trips. It's a fascinating place both historically/culturally/socially and also scientifically/architecturally/financially, etc.
Asian Art museum there is the best I've ever seen anywhere. It's overwhelming to see it in one day-- it's like the Louvre of Asian Art. DD loves the MoMA, the Marina District, just-- everything.
I also love Victoria BC-- for many of the same reasons, though the lack of robust public transportation was a downer there. That's one of the key components in my experience-- exploring a super-rich environment like that kind of requires an avid curiosity and continuous observation-- DD and I
love to travel together.
Recall that I live on the west coast, also. While I love Portland and Seattle both, they aren't quite as kid-friendly as SF was for my DD. The Twin Cities is another great kid-friendly place to do LOTS of stuff that appeals to GT kids. Look at it this way-- much cheaper (and more enjoyable for adults) than Disney.
My favorite eastern US city this way is probably DC, but I've not taken DD to New York, so I can't say whether that would be fun or not. I think she'd like it.
Yellowstone, Grand Canyon and Yosemite are kind of the "don't miss" national parks/monuments, but Zion, Lassen, and Glacier are nearly as impressive-- and much less crowded.
GT kids (high school or otherwise) love experiential learning opportunities, in my experience. That's why travel to some places is particularly lovely.