If you could change your inbound flight to NGO or KIX you should be able to get to one of the islands in the Seto sea on the day you arrive.

I recently stayed at Shiraishi Island, but there are plenty of others that would fit your remit.

If you can't, then from Tokyo there are overnight ferries to the Izu islands (such as Shikine Island), but even Nii Island is a 7.5 hour journey away in a potentially crowded vessel. It would be hard to think of a less romantic start to your trip.

There are also faster ships to Niijima - there's one that leaves Takeshiba bay in the morning and arrives at Niijima 2 hours and 40 minutes later (information source). An easy way to take this route might be to stay at the Tokyo Bay Intercontinental on your first day, this hotel is almost next to the jet foil departure point. If you were to stay there and had a reservation, I'm sure the concierge would be able to help you with pre-booking the ferry.