A week at the Jersey Shore for a family of four now runs between $4,800 and $9,200 depending on whether you pick Wildwood or Cape May. The gap comes down to lodging, beach badges, and how many dinners you eat on the boardwalk. Most families blow the budget not on the hotel, but on the small daily fees that nobody puts in the brochure. Lodging Price Gaps: Wildwood vs. Ocean City vs. Cape May You are not choosing a town. You are choosing a price bracket. The town you pick determines whether you spend $180 a night or $650 a…