Welcome to the forum, msingAUS.
"Here's to another good year ahead, saying goodbye to the previous, and to all the things you've wanted to accomplish in the future!"
A pedant might insist that you were saying goodbye to all the things you've wanted to accomplish in the future. This could be avoided by changing it to '... and here's to all the things ...'.
Personally, I would stop sending cards to anybody who questioned the grammar of my wish.
Student or Learner