Two of my very favorite places to eat in all of WDW are right at the Polynesian - Kona Cafe and Ohana! Both are wonderful for dinner. Ohana has a really fun "family" atmosphere that would make for a really memorable birthday. Kona has incredible food and out-this-world desserts!
Artis Point is another option. It's at the Wilderness Lodge. You could just hop the monorail to the MK and then take the boat to the WL. It's a little quieter and more grown-up, but I've seen lots of kids there, too. The food is amazing. Plus, you could wander around and check out the WL grounds and lobby. If you haven't been there, it will take your breath away. I had my birthday dinner at Artist Point last year and it was wonderful! Whispering Canyon at the Wilderness Lodge is tons of fun for birthdays, too. The BBQ is great and the atmosphere is fun and rowdy. They do lots of silly stuff to embarass the birthday person. It's great! The kids would love it.
Any of the places in the Contemporary or Grand Floridian would be good choices, too. There are fun character meals as well as more adult meals in both resorts.