For 11 to 16 yr old boys, Exploris with its new format would be WAY too young, but it does have a REAL imax theater. They may find Museum of Natural Science not to be too exciting too, although it does have dinosaur bones, including one with a heart.
To me the more interesting museum for older kids (and younger) is the museum of Life and Science in Durham. They have little kids things, like the train, but also some cool weather, engineering and space exhibits inside. And the insecterium is awesome at any age. I love going to that museum and I am 52.
The Rembrandt show is at the Art Museum, so if your kids are into art and history at all, that would be a great show to see as it is the only west coast show. And there is a great hike in the museum property with art AND a cool cloud chamber, where you get inside, let your eyes adjust and see the cloud reflected on the floor. My kids (older like yours) think it is way cool.
The Pit is a good option for BBQ, but get there early or get reservations. It tends to be crowded.
Out by RBC you will be near Umstead State park which is a great place to hike. Another great hike, and different, is Hemlock Bluffs townofcary.org/Departments/Parks__Recreation… It has a stand of hemlocks (only place to find them in NC...maybe east coast) because of a very wierd micro-climate on the property which is fascinating. And if nothing else, its a good short hike.
Let us know when it gets closer and we can tell you if anything is going on that weekend that would be fun to participate in.
Oh, and if you like going to the "local institutions" you could also visit "Hot Weiners" aka The Roast Grill http://roastgrill.com/ The Man vs Food guy and others have visited there. Just don't ask for ketchup.