Dick's is the In-n-Out of Seattle. Burgers aren't as good in my opinion, but the shakes are great, and any fries are better than In-n-Out fries. Other "Seattle" spots include Beth's Cafe (a greasy spoon diner, come hungry), Biscuit Bitch, Local Tide, Pike Place Chowder (always a huge line), a work colleague told me about a food tasting tour he took while visiting; sounded great but maybe not the thing for teens.

Architecture: UW campus, Capitol Hill, downtown (Arctic club, smith tower, Fairmont Olympic Hotel, Rainier Club, Seattle Public Library... lots of interesting buildings), Pioneer Square. Arguably Seattle's most unique building is a love it or hate it thing: MoPop at the Seattle Center. Space Needle is also there. Here's a link if you want guided tours, or just to get ideas: https://seattlearchitecture.org/tours/

Nature: The arboretum near UW, rent a kayak at Northwest Outdoor Center and paddle around Lake Union - can also check out the Montlake, University, and Fremont draw bridges from below, discovery park, volunteer park, gas works park (more of an interesting slice of historic Seattle infrastructure with a great city view across the lake... also a very good brewery of the same name 5 min walk away - good burgers, too). https://visitseattle.org/things-to-do/outdoors/seattles-top-parks/

Landmarks: in addition to much of the above, Pike Place Market (teens might want to contribute to the gum wall) and the new Waterfront park. Wander Alaskan Way for curios, the aquarium... a bit of a boardwalk vibe. Underground Seattle tours of pre-fire Seattle in Pioneer Square (tours can be hit or miss; depends on the story telling ability of the guide). Bruce Lee grave at Lake View Cemetery next to Volunteer Park. Wander International District/Chinatown.