Well if you are looking outside NJ for a shore home, that's a LOT of coastline to consider. You really should contact a local realtor in the areas you think you want to live and get an idea of what's available. I have a feeling that anywhere along the Atlantic shore, the home prices are not going to be anywhere near $250K max budget unless it's a fixer-upper or a condo unit..
Have you seen the prices of even small homes along the Jersey Shore? You pay a premium for the priviledge of being near the water just about anywhere you go.
Here's a link to Coastal Living web site. May have some good suggestions for you:
Here's a link to a site called Walk-Score. You just enter an address (or town) and it tells you whether it's a walkable community or not.
Reach out to me via Trulia or my website and I"ll send you out some suggestions.
George "SERVICE" Conklin 973-248-9293 Jerseygeorge@aol.com
REALTY EXECUTIVES office 973-575-6700