Hey, I lived in the area for 7 years (before I began detecting). I have checked since and this is what I found.
Coin Beach- from Indian River Inlet north 1 mile to the old Coast Guard station. After a winter storm, they find some old coins from a shipwreck. Legal to detect except for the dunes.
Town beaches- Rehoboth/Bethany legal to detect but fill in your holes, these are family towns. Rehoboth has a special men's beach at the south end that might be a good bet for gold.
State Park beaches- Cape Henlopen, Indian River, Fenwick - Check the DE DNR website, but basically you can detect the beaches but not any other part of the parks. At Cape Henlopen, there are some potential unexploded ordinances in the dunes and around the old army base. I would suggest checking in each day at the ranger office to tell them what you are doing. This cuts down on the hassles.
A must see tourist stop. There are three treasure museums in the area. One in Lewes with some finds from the De Braak, one in Georgetown at the community college (50lb ingots of silver from the Attocha). By far the best one is in Fenwick Island, the Shipwreck museum is in the same pink building as the Seashell City. They have an amazing collection of finds from the area. Get the owner to show you some chains from his vault.
Good luck.
Fathead