From experience Especially if they have a part- time or full time job as this becomes the perfect excuse for not going away with the family.

To keep your teen enthusiastic about travelling with the family, you might like to consider involving them with the planning of the holiday. If they have some say in the destination there will be more likelihood of them wanting to accompany you. 

Firstly you should establish whether they interested in going with you. Let them know of your budget. And perhaps give them the opportunity to invite a friend.

There are many locations out there offering a huge variety of sporting / leisure activities aimed at teenagers.

There will come a time when they don't want to go away with their family [you may be at that stage now] they want to go away with their friends.