I am a Japanese living in southern Kyushu and I love Rebun. Though I have been to Rebun only once when I was young (30 odd years ago), but that is the best place I have visited within Japan.
I know there is night train to Sapporo, then a train or flight to WakkanaiNight train to Sapporo from Tokyo takes long time and is more expensive as compared to airfare.
air from Sapporo to Rishiri/Rebun.At this time, there is no flights to Rebun. Rebun airport is now closed. There is one flight per day from Sapporo's Okadama airport to Rishiri, operated by Japan airline.
I think there was a flight to Wakkanai from Tokyo as well. Yes. All Nippon Airways (ANA) operates one flight from Haneda to Wakkanai. There are two flights from Chitose to Wakkanai by ANA.
I might consider using a JR Pass as I might go long trips beside Tokyo and Hokkaido.It takes about 14.5 hours from Tokyo to Wakkanai. If you like train travel, it might not be so bad. But for many, if not most, people, flights should be much easier.
If you get Staralliance Japan Airpass,
http://www.ana.co.jp/wws/us/e/wws_common/fare/special/airpass.htmlyou can fly at 10800 yen per one leg. If your flight to Japan is not by Staralliance airlines, you can use ANA Visit Japan fare,
http://www.ana.co.jp/wws/us/e/wws_common/fare/special/visit.htmlwhich is somewhat more expensive.
You should note that the trip to Rebun largely depends on the weather. In general, good season is June to August, but even in these months, weather changes day by day. I recommend you to take a flexible schedule: Stay at Sapporo and when the weather is getting good (you can predict 2-3 days before), change your flight schedule to adjust for the fine days in Rebun. If it rains in Sapporo, you can enjoy something in the town, but in Rebun, you will have nothing to do in the rain. The air passes allow changes of flight days except for the first flight. Get Staralliance Japan Airpass (3 coupons) and 1. fly to Sapporo and wait for the good weather. 2. Fly to Wakkanai and take ferry to Rebun. 3. Ferry back to Wakkanai and then fly back to Tokyo.