In Minakami town, SL operate round trip to the minakami station from Takasaki Station on Joetsu line, mainly on Saturday.
you can buy ticket at JR ticket reservation office

<Datetime>
June 2 (sat)
lapid SL retro Minakami
Takasaki 9:56 →Minakmi 12:03 (arrive)
Minakami 15:20 →Takasaki 17:13(arrive)

June 9 (sat)
lapid SL retro Minakami
Takasaki 9:56 →Minakmi 12:03 (arrive)
Minakami 15:20 →Takasaki 17:13(arrive)

June 16 (sat)
lapid SL retro Minakami
Takasaki 9:56 →Minakmi 12:03 (arrive)
Minakami 15:20 →Takasaki 17:13(arrive)

May 17 (sun)
lapid SL retro Minakami
Takasaki 9:56 →Minakmi 12:03 (arrive)
Minakami 15:20 →Takasaki 17:13(arrive)

<price>
entry Fee: ticket 970 yen ( takasaki →Minakami )　+ reserved ticket　520yen

※stop station
takasaki → shin maebashi→ shibukawa→ Gokan→ Minakami

Click Here For More Info!
http://www.jreast.co.jp/e/