All dining places in all the Resort are great for celebrating birthdays. I had a birthday pin and wore it the whole week. If the CMs at the restaurants see it, they will go out of their way to make it special. If someone is with you, they could point it out.
For my birthday itself, I dined at 50's Prime Time at DHS. My "cousin" saw the button and when she came back at the very end of my meal she had a cupcake for me with a candle & "Mickey" sprinkles all over it. Then had the area I was sitting in sing Happy Birthday to me.
Once they know it is your birthday, you find a lot more magic. Autographed picture of your favorite character with balloons, getting sung to by strangers, kiss from female characters and so much more.
Have fun and an early happy birthday to you.