Write a letter to my neighbors?

I say forget the letter. A letter is only going to fuel the situation, in my opinion. No matter how nicely it is written, no matter how good the intentions, formal letters don't really have the effect we usually want them to. If you are serious about getting along, next time you have a BBQ, invite them over and try and socialize. Offer them a couple of beers, get to know them and let them see your family as the fun loving wholesome family that you are. If that doesn't work then you are just going to have to accept that your neighbors suck!