Yep, as someone else put it -- "the gift of time." Take her out somewhere -- to a movie, even better, to a play; to the mall if that's her thing; if there's a Lego store near you, make that an option: I'll take you to the Lego store if you want and you can pick out anything there that's $45 or less. And so on. She probably will like the attention.
As for American Girl,you say your budget is $40 to $50 and also say that AG doll clothes are outside your budget -- but AG clothes, depending on exactly which outfit you pick, are about $22 and up per outfit; you probably could get her one outfit plus an accessory kit or even two outfits and still be around $50. You're in New York area -- why not take her to American Girl Place in New York and let her pick out that $40-$50 worth of items? Just a possibility.
Another idea is a magazine subscription! There's American Girl Magazine which is very good and she might like that. Subscriptions keep on giving all year. Find out if there's another she might like -- National Geographic Kids, Kids Discover, etc.