I think I will do that very thing to honor the tree. I will find something and plant it for my little patio. I've already got container gardens out there. Now, I will find a tree.
Trees give a lot of ambience to a place and it's a shame when they get cut down, however some have very powerful roots and when they start damaging the foundations of buildings there is no other choice. Those that planted them never thought about the problem, they could have used another type of tree with less intrusive roots.
I understand the logic behind the decision as it was too close to the building. However, that does not make the loss any less.
My yard is filled with large trees. It makes my house look so small. I love the trees, except in the fall when I have to rake leaves for months. There are several kinds of oak trees and some very unusual pines. Two kinds of maples, dogwoods, walnut, and some more I don't know the names of. A few fruit trees also, cherry, apple, pear and peach. Birds everywhere.