The Ajishima line runs to Ajishima (unsurprisingly), but its most popular stop off is Tashirojima, aka cat island.
This is the easiest of the two Ajishima Line Ports to reach by foot, as it is only 10-15 minutes from the train station (you can also catch a Miyako bus from stop two at Ishinomaki train station, with buses timed to match ferry departures, but it isn’t much quicker). Boats run three times a day and it costs ¥1,250 each way for the cat island. It takes a few minutes to buy tickets (via vending machine) from the ferry office, so ensure you have time and that you have cash as cards are not accepted here. There are plenty of leaflets available here and it’s right beside the Manga Museum as well as the local market, Genki Ichiba.