Hi C.,
Ah, the big 16. I'm a young mother, but I have sisters that have recently enough been teenagers. They have done some creative and fun things that don't cost a lot. I'll just list the ideas for you. :)
1. Thrift Store Party - guests are required to wear the weirdest outfit they can find at the thrift store for $10 or less. If she doesn't like this one try it again when she gets to college. For some reason college kids love weird things like that.
2. Let her go sky diving and her friends can watch her come in from the ground.
3. Disco - disco music is really fun. It seems to relax people. Just so long as they don't start dirt dancing.
4. Masquerade - This could be really fun. People can dress up, reuse those homecoming and prom dresses. Serve hor doeuvres and other "fancy pants" foods. Have her favorite music playing.
These ideas can work with her friends or your family. My family and I adore to be silly and have fun. It forms stronger relationships and is just plain fun. I hope this helps you out. I still remember my 16th fondly and it was pretty simple. It was a good old surprise party. I also got to go on a date with the guy that I had a crush on (his birthday was at the same time so it was a dual surprise party). I have to say though, he wasn't a good date and I remember the party being much more fun. So, no matter how much she whines about it, she'll like it in the end and have fond memories. I think whining comes with the age. My sisters and I totally did it, don't know why, but we did. Have fun with this! :)