What type of shade tree does not have roots that damage side walks, and does not kill grass?
Thus far I like the Chinese pistache tree, but what other options do I have?
Chinese pistache are great medium size trees, and also consider crape myrtle, and mimosa (silk tree).
But you have stated two very difficult requirements.
Most trees and grass don't mix, one or the other or both will suffer in the long term. The frequent watering that is required by grass can cause root rot in trees. Southern magnolia, maples, elms and willows can tolerate more water and may be the best for a lawn area, but may not be root compatible with the sidewalk.
Planting in close proximity to a sidewalk can invite damage from any tree roots, but the pistache and crape myrtle and mimosa are small enough trees that they shouldn't be a problem unless the tree is planted too close. Stay 10 to 15 feet away from the sidewalk, water deep to encourage deeper rooting. Frequent and shallow lawn grass watering encourages shallow rooting of trees.