I used to go to this market everyday and it was really good but now that there is a new owner things changed. Change is not always a bad thing but in this case it is a horrible thing. I never find fresh fruits anymore. The place is dirty now because they fired some workers to save money. Overall unless things change for the better I would not recommend you shopping there.
While I agree with the other poster's comments that the Eastern Market is a busy place, we disagree about it not being appropriate for small children. Yes, it's busy but hold hands, use a stroller, or (our option) carry your child in a carrier like a mei tai or sling. My three kids were perfectly safe and love the hustle and bustle of the market. Be sure to bring your own bags and cash, as that is usually the only accepted form of payment.
This is a great place to shop, but is too crowded to bring younger kids, especially on weekends when they have the best selection. Older kids might be entertained by the fruits and veggies. It would be easy to lose a kid with no stroller, and strollers are hard to push through the crowds.
Eastern Market is especially fun for all kids. It is an open-air market that sells a little of everything from fresh fruit & veggies to cheeses, meats, flowers, arts & crafts. The market is open on Saturdays and has special events throughout the year. My daughter especially loves Flower Day in early to mid May. Not only are there annuals, prennials, baskets, & shrubs for Mom & Dad...there are childrens events like...face painting, flower pot painting, train rides, crafts, and there are even funny clowns. There is a wagon decorating contest that is fun for the family as well.