For someone who wants to discover and learn about Japanese food, this renowned market is absolutely wonderful both in terms of the variety and the quality of the goods on sale. If you're up for new experiences, go crazy and try all the dried little fish (a lot of the time you can sample them for free), the pickles made of everything from cabbage to daikon, the rice cakes, rice crackers, etc.
Typical regional delicacies are the takoyaki and okonomiyaki, both of which I love and would suggest anyone try them. I have yet to meet the person who didn't enjoy okonomiyaki, and though people are sometimes (understandably) a little apprehensive about octopus tentacles sticking out of dubious-looking fried balls covered in powdered seaweed, I assure you, I would kill for some takoyaki right now. (Metaphorically speaking, of course).
There are lots of little restaurants and cafes around the shopping area, which itself is a cluster of streets sprawling outwards from the centre, and there you will find local and foreign cuisine, as well as the little cafes where I found pumpkin cake amongst other things. Another favourite.
Along the actual market street, you will see a couple of little booths or stands where they serve the takoyaki or octopus balls that I've been praising, and you should probably take the time to try some on your way. A word of warning -- you can't really eat standing up on the street, so they'll make you sit down on a bench available where you buy the stuff. Often they also sell a dessert which is fried dough filled with sweet red bean paste. Sounds like a doughnut but it's not as greasy.
As with most things in Japan, some of the delicacies can be quite pricey but you won't find yourself spending a fortune, or if you do, it'll be worth it. It's food, after all.