Anyone know how to give your neighbors a gift and where exactly they are located?

I'm not sure that you can. I think they just send you emails.

There is not any gift giving to your neighbors. Although your neighbors will "give" you stuff or help you out in certain ways, It doesn't seem to work the other way around. It is the one instance you can be a taker and not have to be a giver.

In the game guide it says "Your neighbors can sometimes be very generous and thoughtful, and you dont always have to purchase some of those extra items for your family."

My neighbors bought me new sheets

Yes, DDand50252, the neighbors will sometimes give you things, but there isn't a way in the game for you to actually buy gifts for your neighbors. You will sometimes encounter events in the game where one of the family members has helped a neighbor, though.