We've been on my DD's birthday several times (hers usually falls over their spring break).
She loves Sci-Fi Dine in Theater, so we usually plan lunch there for her. So, I'd take a look at some places your son may like, ask him what sounds fun to him.
This spring, my DH didn't come along (just me and DD) so he surprised her with a gift from Disney florist of balloons and stuff - it was a (overpriced in my opinion) birthday package - came with a cake, personalized ears, and a stuffed Mickey. It was sweet of him to do it, even though I thought it was a lot to spend. They have things like cinch sacks and coolers and things you can add on, and they'll deliver to the room for a surprise.
The day we checked in, we were super tired, and I was kind of grumbly about having a room that connected to another (and the other guests were noisy - I actually called security to quiet them down twice), but then we had a knock on the door. A cast member had a card and little balloon for her - it was noted on our reservation that it was her birthday. That totally made the check in day so much better!
I think 11 may be old for the pirates thing? I'd think more like 6 or 7 for that, but you know your son best.
Anything at Disney on your birthday can be a celebration!! My DD had cast members tell her happy birthday the whole week!