I watched an interesting program about gift-giving once where they got two classes to do gifts for their teachers, one 'however they felt like' and the other according to a list of gift-giving guidelines. The teacher was much happier with the gift from the guidelines, because it was so much more personal and more meaningful.
I don't remember all of the guidelines, but I do know it started with a list of what you know about the person: what colours she tends to wear, what kind of car she drives, what books she is drawn to, what is important to her, what she's particularly good at, food preferences... etc.
The list is really important, and the more you can add to it the better, even weird quirky things are important.
The next part was about what you particularly appreciate or like about the person, because what they like is only half of a gift -- to be meaningful, really, it needs to obviously and visibly be 'from you.' Not, 'anyone who knew me could have given me this.' For that reason, it also needs to be a gift that you can uniquely add to: some personal talent or skill or knowledge that others wouldn't bring to this gift for this person.
Here's one I did for my sister, who lives a long way from our hometown: a set of three images of our old house, from a photo of what it looked like when we lived there -- a line drawing, an acrylic abstract painting and a watercolour painting. I know she was attached to that house (unlike me and my brother, we lived there when she was born and it's the house she moved out on her own from)... and she knows I'm an artist. My mom made her a scrapbook of photos of her from her childhood, including stories and songs and memorabilia from our lives -- so she could have a part of her past with her in her new home. My mom knew photos and memories are important to my sister, and my mom is a big paper crafter -- I couldn't have done it, I don't have the stuff or the techniques to do it.
So... someone who knows a teacher is into international cuisine could give a gift certificate to a funky, new ethnic restaurant that they know about because they know some of the staff, or live close to it, or did an article about the owner. Or, same teacher, same interest: an avid cook could give a 'meal kit' of all the exotic spices and unusual (unperishable) ingredients needed for a personal favourite recipe. A cookbook author could name a recipe after the teacher, include a dedication in the notes about the recipe, and give the teacher a framed copy of the page proof.
It really is about getting as personal as possible -- from both sides.