There are daily bus services to/from Tokyo (9½ hours), Nagoya (5½ hours), Kyoto (3½ hours) and most other major cities from the bus terminal.
Takamatsu has regular rail links to Honshū. There are frequent trains to Okayama (¥2030, 55 minutes), where you can connect to shinkansen services that will whiz you to any of Japan's major cities in just a few hours.
From Takamatsu, tokkyū trains on the JR Kōtoku line run southeast to Tokushima (¥3360, one hour); the JR Yosan line runs west to Matsuyama (¥6390, 2½ hours); and the JR Dosan line runs to Kōchi (¥5360, two hours). The private Kotoden line also runs direct to Kotohira (¥620, one hour).