I like Dave's idea of the book with his e-mail address.
I just completed my seventh trip with OAT/GCT and it was the first one that the hostess opened the gifts in front of everyone. All the other trips we passed the gifts to the hostess when we arrived and they disappeared into another room.
It is interesting to see, or hear about, what others bring. No one on my trips has ever brought T-shirts. I don't my myself because 1. they add weight to my luggage and I try to go light, and 2. I've wondered who would likely wear the shirt? I don't think it would be the hostess who has probably done the cooking. Ditto for baseball type caps. Kids might like them but you don't know ahead of time if there are kids.
In Morocco our hostess showed us the refrigerator covered with magnets from different states.
I usually bring a small box or package of candy, thinking that it's something that the family could enjoy. In Turkey I bought fresh figs at a market for the gift. I read one report that someone had brought fresh fruit (I think it was China trip) and the family was delighted. I have also read that someone brought a cooking utensil. In Buenos Aires one woman brought fresh flowers and a man brought a bottle of wine; the hostess seemed happy with both.
On all my trips with visits to schools, the gifts were given to the teachers, never directly to the students.