Which state of India does not have its own High Court?

The High Court of a State is the highest court of the State and all other courts of the State work under it.

 Goa, Arunachal Pradesh, Mizoram and Nagaland does not have its own high court

The Union Territory of Mizoram and the Union Territory of Arunachal Pradesh are the two union territories which are called the Gauhati High Court. 

In the North-Eastern Area Act, of 1971, a common High Court was established for the 5 North-Eastern States and 2 UTs