Urban trees can be almost any variety that will survive with care. From the woods, you generally get something adapted to the area.
Means that you have to take a chance on species, if an urban tree, though white-barked types are generally pretty bland compared to the "yellow" birches. They also have a relatively short suitable period when spalting. Once they start, they move to unusable within a season. Get the log up off the ground to preserve your spalting options and take a sample foot or two to see what's there.