
Linden can work here, with caveats. American basswood is native throughout Indiana and common in mixed mesophytic woods across the central and southern parts of the state. Littleleaf linden is European and one of the most heavily planted street trees in Indianapolis-area subdivisions — often in rows of identical age, which means their structural problems all arrive in the same few years.
Aphid honeydew is the complaint that actually drives calls — cars, decks and patio furniture under a linden get a sticky varnish all summer that then turns black with sooty mold. On top of that: papery bract-and-nutlet clusters after the June bloom, beetle-chewed leaf fragments through August, and a normal leaf drop in October.
Shallow, dense and fibrous, colonizing the top foot of soil aggressively — this is why turf never establishes under a mature linden and why roots surface in lawns on central Indiana clay, which keeps them shallower still. Basswood suckers off those lateral roots, so a mowed lawn can develop a ring of shoots ten feet out from the trunk, and narrow tree lawns get heaved.