$20 is doable. $35 is over budget.
Definitely forget National Geographic for kids. Lame. What about just plain old National Geographic? When I was a teen I read “Astronomy”, “Discover”, “Popular Science”, “Psychology Today” , “Utne Reader”, and “Smithsonian”, but I used to get beat up alot for it too.
Do you know anything about her? You say her parents are academics but what is the girl interested in? In what academic area does she excel? If you find this out, then go to Borders or Barnes and Noble or something and browse through the magazines, perhaps you will stumble upon something that would fit her.
Science:
Discover
Scientific American
Less science and more history:
The Smithsonian
American Heritage of Invention and Technology
Forget Popular Mechanics and Popular Science. They were okay back in the 70’s, but that was then. Now, they’re thinly disguised advertisements. That ship has sailed.
At that age I subscribed to Discover and Smithsonian. And for a while in high school Science News but that being a weekly, I just didn’t have time for it.
They were both good but I think for someone of general smarts I would most highly recommend Smithsonian. It covers sciences and social sciences as well as very relatable technology stories (I still remember an article about just-in-time delivery systems at the Giant grocery chain, back when the idea was pretty new, mid-80s) and some coverage of the arts.
For something a little different, you might try Mental Floss. It’s only put out once every two months, so that might help with the budget concerns. I think most readers of the Straight Dope would find it interesting, as well.
I just got my copy today. On the cover it says “Plus: Why you never got that flying car you were promised”. It must be fate.
Subscription rate is $21.95 per year (6 issues).