A little bit of on-line searching finally led to me figure out what kind of tree I have in my backyard. It had always been a mystery to me and last night it dawned on me to pluck a leaf and use it as a reference when I looked it up online. I discovered the tree is likely some sort of hawthorn tree. I also discovered I was a tad allergic to it since I was hit with a runny nose and a short bout of sneezing after rolling the leaf through my fingers while I searched for photos.
My only difficulty was that there are apparently many many types of hawthorn trees and they are not all definitively classified. So in terms of what specific type I'm thinking its a snowbird hawthorn. At any rate at least I have a pretty good general idea of what it is. I'm not sure how old it is but assuming it was planted when the house was built circa 1981 this guy is a bit on the old side as the average life span is 40 years or more. But I expect I will still be able to enjoy for a while longer at least. I suspect its a tough old tree having survived a freak spring snow storm a couple years ago and my pruning efforts earlier this summer.
Everything else I read up about the hawthorn seemed to fit....great shade tree for small backyards, low maintenance (I especially liked this part) and small white flowers (although with all the rain I had earlier this summer they never really bloomed the way I had hoped, likely due to all the rain).
I can also vouch that they make awesome birding trees with plenty of shade and a thick canopy for small songbirds to take refuge under.