Most neighborhoods are experiencing brown spots. Big brown spots where debris was once piled up for weeks to maybe months. How long you see the lingering spots depend on what you do.
Maybe you could wait and hope the grass fills in. This might happen if you can detect yellowish green runners or new turf shoots starting to sprout. Where the piles were lose and some turf survived these areas may fill in or their own. Or they could grow weeds.
Residents with big brown splotches in their turf can help them turn green by filling the voids with patches of sod or plugs. Sod gives the best coverage and hides weed seeds that might be ready to sprout. If you choose sod, loosen the soil prior to adding the new turf. You may also need to remove some soil to help the sod match up with the level of the existing good turf or sidewalks.
Plugs are an option for the small areas that can fill in quickly. Usually plugs are spaced eight to ten inches apart. You can find plugs at local garden centers or if you only need a few, cut them out of existing established turf in your yard. Make these into about six inch squares for replanting in the open areas eight to ten inches apart. One more option is to cut sections of sod into plugs and use these to fill the brown spots.
One problem with plugs is you are likely to need weed control. Plenty of seeds are ready to sprout so plan to do some hand or spot weeding. Some non selective herbicides labeled for use among growing plants can be used to hit only the weeds you want to kill. Makes sure the product selected can be used among turf. Then follow the label to make sure you do not harm the new grass shoots.
Your plugs or sod patches need new turf care. Keep the installed areas moist and apply a light feeding in about three weeks. With good care your once brown spots can be green like you remember before the September storm.