Kutchan is on the JR Hakodate Main Line between Hakodate and Sapporo, but it is only served by local trains. From Sapporo it takes two to three hours, requiring a change of trains at Otaru, at a cost of ¥1790. It takes 3 to 4 hours from Hakodate with a change at Oshamanbe.
From Niseko's Hirafu ski fields, Kutchan is an easy 15 minute bus ride. During the day, Donan and Hirafu bus companies operate regular services to Kutchan, one-way fare is about ¥380, depending on where you start and end. The bus will drop off at several points within the boundaries of the town, the terminus being at the JR rail station. Details are in the trail map of the Niseko United. In the winter months, there is also a free Kutchan Night Go Bus service, which runs approximately once an hour from 5pm until 11pm. Strangely enough, to board the free bus, you need to get a free "Kutchan Bus Passport" which is available at all information centres and most hotels.
Walking is a good way to see the sights. The town is not so large that you cannot get to most of the points of interest on foot.
Footpaths can become dangerously slippery during winter. A set of boot "chains" or strap-on cleats will be a great benefit.
First thing, collect a "town map" from your accommodation. Use it to locate some of the places you'd like to see. Then go for it!
Max-Valu, Co-op and Homac (a Bunnings clone) are worth looking through just for the fun of seeing how the locals live and buy.
Browse the shops, look in the "¥100 shop" for bargains, check out the souvenir shops, Takiguchi sports (if you want to get a new set of skis while you are here: Mr. Takiguchi also owns the infamous Seico-Mart in Hirafu), Boom (for snowboards), and the furniture shops.
The main Post Office, at the far end of the business district on Ekimae Avenue, has an ATM that will accept overseas cards (but not if they are other than rectangular!) for withdrawals if you need extra cash.
Just about anything! You can get food, hardware, tools, ski gear (wax, bindings etc) and some wonderful kimono fabrics at Cocoroya on Ekimae avenue.
Find a restaurant anywhere in the town. Most will have a range of local produce, some will speak English (eigo) but many will not. Still, the universal pointing language will often get you what you want. Portion sizes are quite variable, as they are throughout Japan, so be prepared to order more if there isn't enough first go round. It is almost expected.
Miyako Street is worth a stroll at night, for a small town version of a Japanese drinking district.
There are lots of opportunities to sleep. Just walk along the first street from the railway station parallel to the tracks. There is a Hotel with Onsen (Traditional Japanese Bath) about 1km from the railway station, first go south, then head over the bridge that crosses the tracks and river, then walk uphill until you see the sign of the bath. The Onsen is open all night for Hotel guests.