How big?

I planted a 5 gal. fraxinus pennsylvanica (Green Ash), a fast growing native, which is growing by leaps and bounds. Its a good tree because its a vigorous grower when young and although it hits 50-60 in height and 20-30 in width at maturity, it won't displace your concrete sidewalks. Despite its fast growth rate, candidly, I wish I had bought a larger, tree. Then I'd have a pretty substantial addition in just a couple years time.

A quercus palustris (Pin Oak) is another fast growing native that will grow larger than a Green Ash (add 20 feet to height and width). Like a Green Ash a Pin Oak does not have an invasive roots system, so it won't displace your sidewalk, either.

Both trees transplant easily and tolerate a wide variety of soil conditions.

Both trees live a long time, about 75 years.

The native tulip poplar is a handsome tree, too. A fast growing hardwood, VERY tall (over 100 feet, I think). People say they're messy, but that puzzles me... the one we planted doesn't seem to make a mess. It was about 10 feet tall 2 years ago, and is easily 20 feet tall now.

Dawn redwood, aka "Metasequoia glyptostroboides", aka "Dinosaur Tree".
Growth rate: 1 to 3 feet per year.
Fine needle pin foliage, but not evergreen.

Here is a link that might be useful: Dawn Redwood information

I'lll second the dawn redwood suggestion. Sycamore is another fast grower that gets large but is not prone to breakage.

Alex