If you are in Matsue you might as well go to Izumo which is the next station to the west. About an hour by train. In Izumo there is a very ancient shrine which is very large and simple. A short bus ride away is a lighthouse with some wonderful views of the Japan Sea.
This is a must, if you have the time and the money. A couple of days in this area is certainly worth the expense in time and money. There is a beautiful shrine in Nikko which unlike Ise and Izumo is extremely decorative. Interesting walks along the river to the “abyss”.
Take the Shinkansen to Tokyo and change at Ueno station to the JR Nikko line to Nikko. Or from Tokyo station take the Yamoto Line to Ueno and then the subway to Asakusa station and there change for the Tobu-Nikko Line for Nikko. You may have to change at Shimo-Imaichi. The limited express is a wonderful train but the views are not very exciting. Figure three and a half hours to Tokyo and two more to Nikko.