The Oxford City Market (the one that is on Tuesdays and is out on West Oxford Loop) has already commenced and will be there tomorrow from 3 until 6:30. They list the vendors they expect on their website. I went last week, and got pretty marble-sized white turnips, lettuce, and Spring garlic. There was much else.
The Mid-Town Farmer’s Market (the one in Mid-Town Shopping Center by Big Bad Breakfast and Sears) will start this Saturday, May 3rd for what I think has to be about its 15th year. You can sign up for a weekly update that will tell you some of what they expect at their website.