For a new neighbor, some of the best gifts to be given are crockery items such as cooking materials, dish set, glass set, good paintings, decoration items.
A good gift for a new neighbor would be some home baked treats such as a cake, cookies or maybe brownies, or maybe you could even bake them a nice casserole or invite them over for dinner some time, these are some nice ways to welcome them to your neighborhood.
Why not scrapbook for someone besides yourself. To maintain the personal aspect of scrapbooking, collect and dry native flowers from the recipient's neighborhood. Fix the flowers between two sheets of contact paper. Cut the contact paper into any shape. Attach text and pictures. Assemble it as a scrapbook.
Food gifts are always best to welcome someone new to the neighborhood. If you can not bake then purchase something at the local bakery. It will also promote that bakery if they are new to the city and give them the opening opportunity to ask you about other things in the area.
When someone new movies into your neighborhood you should consider giving them home made baked goods and a bottle of wine. If you are not big into drinking you could give them just the baked goods.
how about a homemade pie, in a nice pie plate with something nice written on the botom, and if your neighbor is very kind and u already no them howabout a little potted plant also