I think it's so cool that you want to do this for your daughter
I'm a single Mom of 2 little people.. thankfully I still have a long way to go before the 16th birthday LOL but yeah.. as a single Mom I can relate to things being tight at times..
I forgot to look if you had stated where you live? However if you live somewhere that will be warm in May.. maybe a possibility could be an outdoors party like a Hawaaii theme?
The DJ is a good idea, as far as other things for them to do.. be careful, because she is going to be 16.. yeah LOL I remember thinking I was all grown up at that age!
Anyway.. outside there seems to be more to do.. limbo, volleyball.. things like that.. As far as food, I would do a BBQ..
2 People you may want to ask for some other ideas... Tiki, she just went to Hawaaii for her honeymoon and if the idea for that theme appeals to you she may have some good ideas to help you out.. and although Dyermaker isn't on this forum a lot anymore, he is a 16 year old male and pretty sophisticated.. he may also have some good ideas as to what would be "cool" for your 16 year old daughter.
Good Luck! I hope it goes well
Oh.. just saw you're in NY.. hmm.. could still work the outside deal?