Ah, another Washingtonian moves to the Big Island. I moved here from Puyallup, Wa. over a year and a half ago. I live near Keaau about 12 miles from Hilo. When I read your message, I was going to suggest you rethink selling your BMW. Motorcycles here are quite a bit more than on the mainland. You have talked to the nice folks at Kiser's in Kpna? They now sell, Kymco, Yamaha, Honda, Yamaha, Victory, and Kawasaki. We have a Suzuki dealer in Hilo.
Actually, I am considering a tw200, xt250, or the new Honda CRL250F. It is water cooled, fuel injected and a bit less than the XT250 I believe. I sold 3 motorcycles before we moved here. A 2006 HD XL883 Sportster, a 2007 Yamaha XT225, and a 2007 Royal Enfield 500 Bullet. I did buy a new leftover Kymco People 150 scooter from Kiser's, and they delivered it to me. My wife brought her 2008 SYM HD200 scooter over. Both of these can handle the highways here, with the SYM being more relaxed doing it.
If you plan on riding up to the observatories, then mayb the fuel injected XT or Honda would be better, because it's like almost 14,000 feet. The routes I have taken to Kona by car are not very high. Saddle Road gets up to 6632 feet. That's a major route between Kona and hilo areas.
Here is a good page that talks about the various roads here and elevations:
Aloha, and welcome to the beautiful Big Island of Hawaii!!