I would strongly recommend you make Epcot your birthday night stop and Drink Around the World.
We generally start in Canada with a nice Moosehead Lager and usually can make it to Germany (and the Spaten!) before the ground starts to spin. However, on our most recent trip we started in Mexico, and the new Tequila bar killed our mileage. We did make it all the way from Canada to Mexico once, but we were younger then.... If you're not into beer, you can get wine in Ireland, France, Italy, and Germany.
If you're staying at an Epcot Resort, you can stumble to Jellyrolls and finish your night there. It's usually busyish on the weekends, and you'll have a great time. Also, the Swan and Dolphin have nice restaurants with great bars in them.
If you do drink in the parks, make sure to designate someone as the chaperon. It is still a family park, and getting knock-down drag out drunk there is generally frowned upon.
Happy B-day!