Short answer: "No." While there are beaches within striking distance of Tokyo, they are all either somewhat unpleasant, insanely crowded, or somewhere inbetween -- certainly nothing honeymoon-y.

As you've surmised, Japan's best beaches by far can be found in deep south Okinawa, esp, Yaeyama (Ishigaki, Taketomi, etc), and while you can't get there from NRT, there are direct flights from HND to ISG if you can deal with the bus transit from NRT (~90 min). Also, don't discount OKA entirely if the few flights from NRT match your schedule; sure, big city Naha isn't what you're looking for, but it's a big island and there are plenty of small islands a short boat trip away that offer a modicum of peace and quiet.