My favorite neighborhood fresh market was a brief 10 minute bike ride from my apartment, so I frequented it fairly often. There was always a bounty of beautiful fresh foods!
Hopping atop my trusty mamachari or "mama's bike", the equivalent of a minivan on two wheels, I'd take advantage of the handy basket and stock up on reasonably priced produce while there.
There was also a small fish market with fresh sushi and prepared fish inside, along with a butcher wrapping packages of meats in cellophane. All your necessary staples were there (as long as you're comfortable with cooking and/or Japanese food), but sometimes unexpected items like grasshoppers or seasonal sweet cakes would appear on the shelves.
Their flowers were among some of the most reasonably priced I encountered; usually around ¥300-700 whereas the somewhat closer Yaoko supermarket's flowers were often twice the price!
One option that makes shopping in Japan more affordable is to visit stores late in the day or evening, closer to closing time. Fresh things, like sushi, precut vegetables, cut flowers, etc. will get marked down and the later it is, the greater the discount. I've had many a satisfying sushi or sashimi centered dinner for under $10! Of course, the people at the fresh market were so pleasant and friendly, and the prices so reasonable to begin with, that I'd make a point to shop there on my days off as their hours didn't pan out on days I had work.