If you're going to remove the Ash right away, then wait to plant a new one, if you're going to site the new tree within the fall zone of the one you're taking out.
Above all, do not plant a replacement tree in that crappy little excuse of a tree lawn where the Ash is currently sited. Do yourself, sidewalks, your neighborhood and the new tree a big favor and plant it as close to the center of your yard as possible, taking sewer lines, gas and water lines into consideration. Call 811 and get a dig tickets so that all the utility companies will come out and mark their utilities, then try to site the tree in a spot where future repairs or replacement of underground utilities won't cause undue harm to the roots of the tree. I typically spend 3-4x the time it actually takes to plant the tree, in assessing the site and finding the best (most sustainable) location to plant it.
If you're going to wait awhile to remove the Ash, and want to plant a replacement tree in a better spot (near, but not directly underneath) the removal tree, you can let the canopy of the old tree shade out the new one, which will encourage it to grow up, rather than out, which will make a big difference in how the new tree develops. Young trees benefit from the shade of nearby mature trees, which encourages excurrent, rather than decurrent growth without the need for the more rigorous structural pruning needs of young trees planted in full sun.