Where to stay in Skiathos?

Doing 4 nights in Skiathos. Thinking on prioritizing beach and one boat tour

Debating between Koukounaries and Megali Ammos. The first looks like the most beautiful beach in the island. Is it worth missing all the great food from Skiathos Town and stay here? Concerned about how far is from everything since we won’t have a car

Megali Ammos seems like a good compromise of beach and near town but the beach is not as pretty?

Any thoughts? And any hotel recommendations ideally under $250 per night. We are going in May next year Thanks!