Rake leaves and pull weeds for your neighbors. Soon they will need help with shoveling snow.
Walk around the town and pick up litter.
Go to the town's animal shelter and volunteer to help care for all the animals.
Go tour local museums and art exhibits to learn more about where you live.
Go to your town's website to see what points of interest and sightseeing places they highlight for visitors and newcomers. Work your way through the list of free stuff to do.