Hi K.,
WOW...it's really hard to find really good neighbors that are so very kind and generous now a days. :-) Welcome to AZ first of all, and I'm so happy to hear that you moved to a place where you have great neighbors!
I would invite them over for dinner one evening, or even for a lunch. You can invite to take them out to eat one evening if you can afford it. Or, get them a gift card to a restaurant, along with a card saying 'thank you for being there'. You can take them a plant. You may be able to see if they like plants by what they have in their house. Also, you can go on "Flowers.com" and send them a fruit basket, or some kind of goodie basket. :-)
I would love to have a neighbor that is so friendly. We have some good neighbors, but most of our neighbors keep to themselves. Hardly anyone socializes in my area.
I'm a stay at home mom too. My son will be five years old come October. I'm pregnant with my second child, due in August. Another boy!!! YAY!!! I'm going to have a house full of testosterone! HA HA HA....
OH, I just had another idea...what about homemade cookies? You can put these in a decorated tin. You can find those at Michael's craft store. Or you can put them in a basket. You can create a basket full of homemade goodies for them. :-) They would probably appreciate anything you can do for them. Perhaps help them with little projects around their house. May be help them with their lawn care etc. Our neighbor is a single mom with a two year old, and works nights/graveyards. She rented the house next to us, and Bless her heart, she had weeds everywhere. It didn't appear that she had any help from anyone to help her with yard care, so my husband and I went out and pulled weeds for her and sprayed them. Even our son got involved and helped. :-) She probably didn't realize that we did that for her, but that's ok.
Well, I guess I had a long winded answer here for ya huh. LOL Hope my ideas helps you some. :-) Take care and Blessings to you and your family!