I agree with Cupid put the ball in her court.
I would also remind her that the world does not revolve around what she wants all the time and everyone has to do stuff for other people. I will give you my example of driving this point home, I like to feel I did it with humour and both my sons think it is funny now.
No I did not want to watch Thomas the Tank Engine again and talk about the troublesome trucks or the island of Sodor, nor did I particularly want to listen to you talk about a tv show or computer game but it was important to you and that made it important to me. I listened to you, asked questions, showed an interest because I love you. I played "your music" in the car, Hi-5 and the wheels on the bus rather than Green Day. Standing beside a fairground ride waiting for that 2 seconds for you to come into view every 20 seconds so I could wave to you, looking at sticks on the floor you are pointing at, listening to talk about your best friend when in primary school, having your best friend (loud and destructive) over for sleepovers or play dates was hard work and not particularly fun, again I did these things because I love you. I am sure your DD can relate to this as she must have done things because her friend wanted to not because she wanted to. It is compromise.
All these things add up to me knowing you, understanding what you enjoyed and what you disliked and now this is me wanting to spend time with you. I am a person, just like you, not just your Mum. I love being with you and want you to spend time with us.
So some things will have to be what other people want and hopefully she can come up with stuff she wants too. It is a two way street, ask her how she would feel if she was really excited about something and you just moaned about the cost or driving her there, moaned when her friends were around about it. She is 16 not 6 she needs to see herself more clearly.