That's going to be tough to find this year. The Easter freeze and then the drought has really cut into crops and what there is costs a lot more.
I was just out Hwy. 11W through Grainger County and there's a pick-your-own farm selling tomatoes for $10 a bushel. In years past, the same place sold them for $5 a bushel. The fields are empty compared to previous years. Even the tobacco is small and late.
I posted a lot of Farmer's Market info earlier on this forum. It's a few posts down. They may be able to help.
There's a pick-your own listing here:
Tennessee Vacation - Pick-your-own Produce Farms
Call before going out to make sure they have something.