The biggest island in Yaeyama islands is Ishigaki island.
It takes 3 hours and 5 min from Haneda to Ishigaki airport. (direct flight)
I used JAL mirage for the flight. 19,000 points to Ishigaki airport from Haneda airport. Usually you can go anywhere inside of Japan with 12,000 so, it takes additional 7,000 points to go to Ishigaki Island. Acually I usually can’t book the direct flight to Ishigaki because of the limited number of the seat for migrage. I think I can book this time because it’s not season to visit Okinawa. What I do is to book from Haneda to Naha(capital city of Okinawa prefecture) with mirage and buy the ticket seperately from Naha to Ishigaki. There are many flights to Naha, so it’s easy to book it.
For the first two days, I'm going to say this hotel, called "Art Box". 1,800 JPY / night. No food. Just stay. But very cheap. I'm allowed to stay this hotel, because I travel alone...