I planted a seedling of one of my favorite trees, a mimosa, 9 years ago in my strip. It's been through alot of turmoil; the town ripped out our aprons and put in curbs; then paved the street. Then, a water pipe had burst near the tree, so the water company may have disturbed the roots. Unfortunately, I'm still waiting for it to bloom...

If anyone else reads this thread, I might get scolded for intentionally planting a mimosa ;)
To each his own...

Tracey - I LOOVE mimosas. The smell of the flower is soo delicious. I want one very badly. I keep meaning to steal seeds but I keep forgetting to get them in season. Unfortunately, they are not very stong trees and don't like our cold winters. Eventually, they seems to break from snow or die. I don't care, I want one anyways.

Ellen

Are there any electric wires overhead?

You should check your town ordinances about planting in the strips. Our town (New Brunswick) only likes to plant the trees themselves. I don't agree with the trees they choose but they worry about the underground utilities (we have gas and water going through our strips) and such. They also worry about whether the tree will withstand salt and plow stuff and other abuses. There also might be fines involved for planting in strips.

Are we talking a two foot wide patch here? Do your neighbors have trees planted in these spots and how big are their trees?
If it were me, these are the things that I would be condsidering. I would assume almost any large shade tree will lift the sidewalk eventually although in my eyes, nothing makes a street more pleasant to be on than large shade trees. I would keep my eye open to other trees that have behaved well around the area. You probably have to look for a smaller tree and/or an upright tree that could be heightened enough for traffic both pedestrians and vehicles. A tree like a magnolia, witchhazel or stewartia are all beautiful but tend to go wide and low. Still, you could probably train one if you really get set on one. Try searching images and see how people train their trees. I would consider planting the tree on your side of the walk were the roots had more room a few feet away from the sidewalk.
Then I would have fun looking for something I really loved.
Mimosas are beautiful trees. They might be good because they are not suppose to live long so it won't damage the sidewalk. They are messy as they drop beans. That is another consideration - if you don't want some kind of messy fruit or petals being tracked in the house on the bottom of someone's shoes since its next to the sidewalk.
As far as what to choose, I have a lot of favorite trees that I love. Why not try perusing through a few picture books like Michael Dirr's Hardy Trees and Shrubs. It's expensive so you can check it out of the library or sit in book store and browse. Beware though. He will make you fall in love with a lot of plants that will take up a lot of garden real estate and you will want his books.
Walk around Rutgers gardens - there are a lot of trees there. Also Frelinghuysen arboretum, the NY Botanical Garden, the Brooklyn Botanical Garden and maybe even Wave Hill. Consider habit for the space, leaf texture, flower or fruit, fall color and bark beauty. If you have a digital camera, you can take pictures of the nametags and then the trees so you know what your looking at.

Anyway, check out the tree forum because they are very opinionated over there.

Ginko biloba - male
acer griseum
Right now, everything I am thinking of is wide growing.
Then there are conifers...

Here is a link that might be useful: sidewalk and trees