The town has opened the new parking lot for State Road Nature Preserve. With room for 12 cars, you should have no trouble finding a space. The town is still landscaping around the lot, so you may encounter work being done for several more weeks.
Note that it can be very wet and muddy getting from the parking lot to the Broken Willow Trail, so be prepared, especially after rains. Friends will be looking at improving that, and other areas, now that the parking lot is open.