Ritsurin Park is located in Takamatsu City, in Shikoku’s Kagawa Prefecture. You can access Takamatsu by train, ferry and plane.
By train, you have to reach Okayama station first. You can easily get there by Shinkansen from Tōkyō, Ōsaka and Western Japan. At Okayama station, get on the Marin Liner Rapid train, and get off at the last stop, Takamatsu Station. The journey price from Ōsaka is about 8.000 yen, including Nozomi Shinkansen and the Marin Liner, and it takes a couple hours.
Note that you can travel with no additional fee if you use the Japan Rail Pass (including the West Japan & Shikoku version), but you cannot ride the Nozomi and Mizuho fastest trains, so the journey time will require some additional ten minutes (you can ride on Sakura, Hikari and Kodama Shinkansens).
Since from Tōkyō it would take about 5 hours, travelling by plane would be probably more comfortable. You can then reach Takamatsu station by bus from Takamatsu Airport, which is linked to Tokyo Haneda Airport.
There’s also a ferry service to Takamatsu from Kōbe port: the one way fare is 1.800 yen, a roundtrip ticket costs 3.300 yen.
You can take a bus from Tōkyō and Ōsaka too.
Ōsaka’s day bus fare is from about 2.600 yen.
Ritsurin park is located about 2 km south from Takamatsu Station. You can walk along the shopping district to reach the garden, but you can get closer to it also by JR line: take the Kōtoku Line heading to Tokushima Station and get off at Ritsurin Kōen Station. The park is 5 minutes walking from there.
Also, you can take the Kotoden tram running through Takamatsu city. You can take it at Takamatsu Chikkō Station, which is close to Takamatsu Station. The park is 10 minutes walking from the stop called Ritsurin Kōen. It’s comfortable to travel by tram across the city.