I think sometimes teens don't answer because they don't really know - this is a time of questioning and change for them. They sometimes are comforted by the types of parties they had as kids (cake, ice cream, parents) but also are feeling a little more independent and wonder if they should not be doing something that is "uncool". If they are in some ups & downs with their friends, they are afraid to invite peers to something that doesn't "measure up" or that their friends might decline to attend. Fear of rejection can be a factor.
Without knowing your daughter's likes and dislikes, it's hard to give ideas. If she'd like a family dinner and is a little bit adventurous, you could do something a little out of the realm of the typical pizza & soda routine. I live in the same town you do, so I'd suggest the Melting Pot (fondue restaurant) in Framingham, or Bocado (tapas restaurant) in Worcester. Both have a variety of menu items and the chance to taste a little of a lot of things. These are places she isn't going to go with her friends. If she likes something a little tamer, there are plenty of neat places on Shrewsbury Street in Worcester. Sometimes just getting out of her own town and not going to the mall is a good thing.
You could try gifts in a "16" theme with a few gift certificates in $16 or $32 - you can do most gift cards from stores in any amount, vs. the purchased cards from the supermarket that are only in the $20 or $25 denominations. If you like the Lottery, you could buy her 16 $1 cards since she's not old enough to buy her own. I'm not a big Lottery fan, but one of my stepdaughters thought this was the greatest gift in the universe.
You could also take one or two of her friends to one of the great museums in Boston and let them take off by themselves for a while - the Museum of Science has some great movies that are suitable for a lot of ages. A lot of teens like the IMAX theater there as well as the exhibits, and there's an IMAX theater at Jordan's Furniture in Framingham too. Not the usual theater fare if she and her friends like movies. If she likes art, the Boston and Worcester Art Museums are great, with a wide variety of exhibits.
Our son's youth group used to take the kids on occasion to the Improv Asylum in the North End - it's an improve comedy club similar to the TV show "Whose Line Is It Anyway". It's not so great for younger kids so if you have plans to take younger siblings, it's not appropriate due to the type of humor. But it's a hilarious performance based on audience suggestions (she doesn't have to participate if she's shy), and then you could go for a nice meal or some great hot chocolate and cannoli dessert nearby. Let her take a few friends and you can sit separately from her! We sat behind our son and 4 friends, and watched them roar.
Maybe if you give her a list of 4 or 5 suggested choices, she can pick one or at least start with one and "edit" it a little bit?
Good luck!