I live in somewhat nearby Akron, and Youngstown is a dying city. Check out one of the more recent editions of Forbes for a full list of dying cities in the United States. There will never be a natural disaster there (unless you want to count the horrible wind damage that just occurred in Ohio, Pennsylvania, Kentucky and New York) and I doubt you will be able to find a very good way to get there from New York, NY. Youngstown used to be a very prosperous city, but has taken one of the most dramatic economic falls of any United States city over the last decade (right up there with Gary, IN). I would not advise moving to Youngstown if you are a senior looking for easily accessible stores or restaurants.
Akron, Medina, or any other cities along I-77 would be a much better bet if you are trying to move somewhere in Northeast Ohio. I guarantee there is an Amtrak from Akron to New York (Akron is about 20 minutes west of Youngstown), but I know that the drive all the way out there would be something close to 8 and a half hours. Public transportation is not very good however in most Ohio cities. I have spend a decent amount of time in all of the major cities (Columbus, Cincinnati, Cleveland, Toledo, Akron, Dayton, and Canton) and none would have what I consider to be above average public transportation and none have a booming economy. Cities like Medina, on the other hand, are booming suburban areas near big cities (about 20 minutes away from both Cleveland and Akron) and would be a good place if you are interested in walking to neat stores and restaurants. The downtown area is quaint and old-fashioned, and the city as a whole is not rundown like Youngstown.