It really does depend on what you're planning to do.
Bear in mind that if you eat and keep it low carb, you still shouldn't be drinking. It's not a great idea to be in ketosis and have a drink - one, you'll get drunk much more quickly and so your resistance to food will be reduced, two - well, there's some evidence to suggest that it's dangerous to be in ketosis and drink alcohol.
So if having a drink is the important thing, then you're going to need to have some carbs that day. If you can do without alcohol, then your best bet is to have a low carb meal.
It's a really tough decision, cos I know that a big part of you doesn't actually want to come off the diet for your birthday, but you'll probably feel under some pressure to do so from well-meaning friends and family. The other thing is the "it's not fair, it's my birthday - I should be allowed to eat!" thing.
There aren't any right answers - but there is a right approach, and that's to plan exactly what you're going to do in advance
and plan how to get back aboard the wagon afterwards (that's if you choose to come off
)