Besides New Chitose Motorland, there is another facility in Hokkaido to enjoy grip driving or drifting. It is Auto Sports Land Sunagawa just north of Sapporo. The facility has a asphalt course and dirt course, the latter being a bit bigger than the first. Free driving with your own car is possible on both of the courses. The course is set up and/or driven as the person that made the first reservation for the day.
It costs 26000 yen to rent one for the courses for a full day (from 9:00 am until 3:00 pm) of free running. It is possible to do it by yourself, but the more people are joining, the cheaper it gets of course. After 5 or more people joined, the price will be 5200 Yen per person per car. It can happen that multiple groups join that day, so it would mean you have to share the course then. In case you do not want this, you can privately rent the course which costs 209500 Yen. The requirements for driving on either of the course are to have a helmet, gloves and long sleeves and trousers.
Season for using the facility is from April until November. Access to the facility is quite good. By public transport, you can go from Sapporo station to Sunagawa station in around 45 minutes, after that it is around 20 minutes walking to the facility. By car it would take a bit more time from Sapporo city center, around 1 hour to 1 hour and 20 minutes.
A link to the website can be found below:
http://www.homei-gr.com/beams/sunagawa/top.html
And a link to the location on Google Maps: