I’ve worked in daycares and taught in schools. I would suggest getting something useful (books, toys, or games for the room) or something truly for the teacher but make it disposable (a gift card or bath salts, note cards etc).
Make sure to include a nice note from yourself and your child. Even if your child can just scribble, let them do so on the card. Talk about what you are doing (getting a gift for their teacher) and why (because you appreciate how they take care of the child). This helps a child begin to understand the importance of showing appreciation. A picture of your child would be appropriate in the card too.
If you’re interested in my rational, please read the following:
Every year there are a number of children that they work with and if they all get them things that aren’t useful, the items will more than likely end up in a garage sale or at Good Will. This has nothing to do with how that provider feels about you or your child, there is just only so much space for things.
Although some may enjoy trinkets or cute little bobbles, most would appreciate something that is more useful. Most Teachers, in the school system, spend their personal money on things for their classroom such as books, tapes, pencils, etc (This happens less often in a daycare setting).
If you know the provider personally, outside of daycare or school, getting a keepsake may make sense. Because of the personal nature of your relationship you should know a lot about their personal space and style and may get them something they would truly love and use or display. If you don’t have the relationship, stick to the fist suggestion.