If you drove to Avon, on average you would be spending $150 in gas. If you flew with a family of 4 on average, you would be spending $1088.
If you would drive, you would have to cross the 5.2 mile bridge over the ocean onto the island. If you would fly, you would arrive on the island at the Cape Hatteras Airport. You would need to get a rental car which average around $560 a week.
You could stay in a hotel or rent a beach house.
To get grocery's, you can visit the nearest Food Lion open from 7am-10pm. The Food Lion has a lot of fresh produce and fresh fish caught in the ocean.
There are also many yummy restaurants around also! Including Ocean Bistro and the Froggy Dog Restaurant all in walking distance.
Typically, on the ocean side most people surf or boogie board. Typically, on the sound its calmer so most people paddle board kayak.
Some places you could rent water sport items is Ocean Air or Wind-NC located on the 12th mile on Avon!