In the greater Chicago area, elm is the most likely answer. Which elm? The short list for this area is Ulmus americana, American elm, Ulmus pumila, the Siberian elm, Ulmus rubra, the Red Elm or Slippery elm. Possibly Ulmus thomasii - the Rock elm, noted for its hard wood. That is pretty much it.
The Siberian elm has the smallest leaf of any elm and is totally shade intolerant. Meaning you will only find seedlings growing in full sun.
The other 3 have larger leaves and these 3 can grow with some shade, though they all prefer full sun. Ulmus thomasii can have corky wings on its twigs, like the ''winged elms'' of the southern states, it is related to the cedar elm of Texas. The Slippery elm or Red elm, Ulmus rubra has downy fuzz on young twigs, the fuzz wears off before the first winter.
Zelkova and Chinese elm both are more ''southern trees'' they have not naturalized in the greater Chicago area. Both do better further south, though they are winter hardy enough to survive if planted deliberately as a garden specimen. They just have not spread and gone invasive in this area. The Siberian elm has gone wild and is a very, very common invasive of open fields.
All elms have leaves that can reduce to very small, all are excellent for bonsai. Even the American elm, which naturally will produce very large leaves, can in bonsai culture have very tiny leaves.
