Plenty of good choices out there; search this forum or google with your subject line to see what's been said multiple times before. I assume you are in northern OH? Here's a few starters.....

Fraxinus americana clones (most are males, no seed)
Ginkgo biloba clones (most are males, no seed)
Gymnocladus dioicus (male clones, no seeds)
Nyssa sylvatica (male plants, no seeds)

Look for dioecious plants (male and female flowers on separate individual plants) and you should be able to reduce the "clutter" that you wish to avoid.

Here's another one, though I'd list it below most of those John detailed above in desirability - American persimmon, male clone.
Oh, and the 'Rotundifolia' selection of sweetgum(Liquidambar styraciflua) is purportedly gumball-less, but I've seen reports of individual branches reverting to fruit-producing phenotype. Still can't bring myself to plant a sweetgum, though.

oops. I think that's probably Rotundiloba, not Rotundifolia.

A little leaf linden tree would be ideal. It is a beautiful pyramidal shaped tree and creates considerable amount of shade. Check it out.