Or you could try to figure out what kind of flowers she likes and get those for her. Normally I would say something like perfume or jewelry would be nice, but in this case - I wouldn't do that quite yet.
If all else fails take her out on a really special date. Cooking dinner at my place (she's never been to my house)? It's only been three dates, maybe four or five if you can squeeze them in before her bday?
If he asks him why you bought it for him, or why you brought him to the new place, tell him you had a feeling he'd like it.
I'd don't think I'd expect something from someone I've only been with twice and I'm sure the thought counts a lot, this first time.
You just started dating him so I wouldn't embarrass him with an expensive gift - what if he only had an inexpensive gift for you? How about tickets for the two of you to go to a Christmas concert with dinner beforehand?
A sexy gift of yourself make a great birthday gift. This might only work if you actually know your boyfriend really well.
Plan a day or a date to do something he says he has been wanting to do. You might have a sense that he is really interested in trying something different, but is afraid to say it for fear of being embarrassed.
I have a HARD time with gifts, but the ones I like could be as simple as someone drawing me a silly, funny picture of something we did together once.