My stepdaughter (age 11) is hard to buy for...she is at our house only every other weekend and most of the summer, but it makes things difficult with her having enough time to actually use a toy or other item we purchase. Last year she really, really wanted a certain dress from a catalog. It was a girl's party dress (big swishy skirt)...she had wished for it for three years. It was out of our budget. Finally, we felt it was her last year being a little girl, plus our $ had improved, so we purchased it. She was over the moon! I was worried we didn't have somewhere other than church to go...would she wear this. We also then gave her tickets to a special night out with us, we were able to take her to see a musical at a big theater. (The certificate we made read: Every beautiful girl with a new dress needs a ball to attend...") This was a first-time experience for her, and very memorable. We also took her out to dinner, not even an expensive place, but one of her choosing. We left the other kids home, so she would feel special on her "date".
After doing this, and remembering a birthday lunch out with my parents when I was in my early 20s, I know that the experience will last long after the dress is gone. I'm not saying go buy a dress...just make the day something meaningful! It can be as cheap a day as you can find, she never has to know the cost!
She also had a special girlfriends' night over. She loves to go to "spa" days, but we limit it to getting a manicure/pedicure. (FYI, she's like a feminine tomboy, so it might surprise you she likes girlie stuff...she's just well rounded. She can beat her older brother at most athletic challenges!)
We have also taken our birthday kids in the past to do different things like canoeing, horseback riding, ice skating, hockey game, etc. Our kids love to have fondue parties at home where we break out the fondue pot, gather round, and cook our meat at the table (their friends have never done this at their own homes, so it is quite a fun experience for all!)
Another special item I own is a piece of jewelry from when I turned 30...my mom gave me a gold bracelet that said "29", the joke being that I was now always 29 (and should never tell someone I was older). Any meaningful jewelry you choose for her 16th birthday would also be special.
I hope you find your special gift and it fits her to a tee!