[ Sure there are plenty of things he needs to do on the Enterprise. But, given that Tony did make him some technology? He figures it's only polite to actually show up and be present at his birthday party. Besides! Free alcohol and maybe he'll find a lovely lady for the evening... for multiple reasons.
With a glass in hand, Kirk wanders around the party to insert himself into any conversation he can find. Hey, he can use a party to gather intelligence from the locals. And he's in civilian clothing since it is a party. ]