Cape May has many of excellent BYOB options
The Washington Inn is known for their wine list (not a place to stay, only a restaurant and wine bar)
Congress Inn looks like a good vibe for a stay/bar/eats
Another place not listed would be Ryland inn. Ownership changed years ago with what seemed to be focus on weddings, but I believe they started doing dinners again.
Sergentsville Inn? Another historic inn. I’ve read the chef is from Momofuko ko, Sean Gray.
All due respect to @TGigante I have not found any good restaurants in Cape May or Cape May Point, where my in-laws spend a week every summer. We never, EVER go out because of the lack of good food available. Come and spend a night with us in Philadelphia on your way to or from.
I never expect fine dining in a beach town but Washington Inn and Peter Shields are very good. There are two Latours up north. One sucks and the other is great. You want the one that Chris points out.
Had dinner last night at Lula (28 Oak Street, Ridgewood, New Jersey 07450) amongst a bunch of Berzerkers as we did a Loire night in the burbs. The seasonally inspired menu was great and we shared a bunch of the menu items even if I forgot to snap pics of everything and they were all well executed and tasty.