A northeast beach that you can enjoy in April; that's a tough one. I think you're probably going to have to go south, like South Carolina. You might be able to get away with the outerbanks in North Carolina, but I really think you would be safer with South Carolina and points further south if you want to enjoy being at the beach.
I just know here in NJ we've gotten snow in April, so I think a northern beach would be tough that time of year.