Bring em over a nice, warm apple pie... straight from the oven. Wear oven mitts. Smile big.
Works great.... !
Be sure to follow up the contact with cheery waves as you drive by or similar things.
My husband will periodically mow a neighbor's yard if he knows they're new or involved with something. Then he stands around with them and jabbers if they're home.
We have some seriously nice avocado trees, so we take fresh fruit around in season. Or I'll make some christmas cookies, put em in nice tins... hand em out. We've had neighbors give or share with us their sausages from smokers, oranges and grapefruits from trees, starfruit, trash barrels, even concrete mixers!
Our neighbors have been there for us when we've needed em... you make good neighbors by being good neighbors - that's what me Gram always said!