Kagawa Prefecture is famous throughout Japan for sanuki udon — thick, chewy wheat noodles served hot or cold, in broth or with dipping sauce. Marugame has a concentration of udon shops that range from stand-up counter restaurants aimed at workers to more formal settings. The local chain Marugame Seimen takes its name from the city (though it is now a national chain headquartered elsewhere), and the original local shops are often better.
The Seto Inland Sea location means fresh seafood is available year-round. Tai (sea bream) and octopus are the local specialties; look for restaurants near the port that post handwritten daily menus. The covered arcade shopping street near the station has a mix of local lunch spots and the usual Japanese convenience options.