Didn't find anything at the local market or the nearby shops on the streets? Tokuzomaru is one of the older businesses that has flourished out of Inatori and has restaurants, and souvenir shops all across the Izu Peninsula. All products are readily packaged so that you can bring home as a souvenir. Would you like taking home Nori(seaweed paper), tokoroten(seaweed jello, yum...), or the local blend fish sauce (tastes similar to Teriyaki sauce)? If you consider yourself a daredevil or an expert japanese traveler, you must have the Shiokara(fermented squids and clams) which comes in multiple flavours.
There's also a restaurant adjacent to the shop which serves such things like grilled Turban shells and the famous "GoldenEyed" Izu splendid alfonsino.
Itterasshai!