Sanuki udon is the local delicacy and it's definitely worth a try; it's delicious! There are restaurants all over, but for a convenient location, there is one in the Yashima area near Yashima temple and the Yashima Aquarium. It's on the street with the souvenir shops; the last building before reaching the overlook area.
It's a nice restaurant, and there are souvenirs there, as well, that you can look at as you wait for them to prepare your meal. It's a great place to try sanuki udon while remaining on track with touring. Yashima is one of the city's best historic areas.
There's an excellent value beer garden on top of the Temmaya department store, I spent a very happy five hours there ripping through enormous quantities of beer.
Great place and excellent value at around 3500 yen for 4 hours.
Kagawa and Takamatsu are good places to sample Udon noodles. Not only are they cheap, but you can also fill up for not much.
Sanuki (the old name for Kagawa) udon is famous throughout Japan, and you may even see the odd bus tour come into town with people coming solely to sample different varieties of udon.
This is not a gourmet place, but if you want to feel like a japaneese, sure you will! Very cheap fast japaneese food (i.e. noodles with a variety of soups and some tempuras) in a single room 3 long shared tables restaurant. Mainly visited by students (there's a big high school a block ago), and local workers, to get a fulfilling lunch in a few minutes.
Favorite Dish: Sanuki udon (thick wheat noodles, typical in this region) with several sliced vegies into a cold soia soup... hmmmm.... not a complex dish but simplicity here makes the difference! Of course, it also does when I payed 450 yen for a two people meal!!!