In South Providence, on Broad St. there's a really cheap farmers' market Saturday mornings. It not just inexpensive for a farmers' market, but I think some produce is cheaper than the grocery store. Items available for $1.00: head of lettuce, 3 green peppers, bunch of basil, 2 onions, 2 bulbs of garlic, bunch of cooking greens, and more! Also available: lemongrass, cilantro, Thai basil, chili peppers, lime leaves, figs, sweet potato leaves, water spinach, tat soi, mustard greens, long opo squash, pumpkins, purple corn, melon, pears, apples, grapes, peaches and plums.
Definitely check it out!