>>281519917
The most expensive up front cost is the flight, assuming you're in north america. They run anywhere from $750 from the west coast to $2000 from the east coast at a bad time. It's cheapest in autumn, between Sept and November, which is incidentally the best time to ride. I wouldn't try Hokkaido after October though, the snow and ice arrives fast.
Hotels will be roughly $50/night, so for 2 weeks you would want another $750
The expense for the bike itself is tricky. Rentals for cubs are generally about $50/day, Rental819 is a good service with good information on their website, however they typically only include a helmet. If you want boots, gloves, a jacket or other gear, you have to decide if you'd rather pack those or buy them in country. Considering you're going to be carrying your luggage with you on your bike, you might want to save the weight and space and just buy them in country (+ ~$300). You will want a dry bag and some Rok straps (+ ~$100), it's the easiest way to carry everything through inclement weather. Many roads are toll roads, and your bike may or may not be outfitted with a toll reader - considering 125cc is the minimum allowed on japanese highways, I would try to avoid these as much as possible, though for certain routes it's unavoidable. It's not a huge cost either way, just another consideration. Eating and drinking can be done on the cheap, but I would budget a minimum of $30/day to fuel yourself. Fueling your bike will be about $100 total (Hokkaido is ~1000 miles around / 100mpg / 10 gallons @ $5/gallon + misc. tolls)
Final rough tally:
Flight: $1000
Hotels: $750
Cub: $750
Food: $500
Fuel, Tolls: $100
Gear: $100-500
Budget three thousand USD, give or take a few hundred. Consider whether this is worth more to you than outright buying your own brand new CT125 at that price!