Hi & welcome to UKY Mary Grace! I'm originally from Ohio, living in South Yorkshire.
I'm not far from parts of Lincolnshire (I live on the Lincolcn to Doncaster train route), and work in Retford, Notts, which isn't far from Gainsborough, Lincs. If you're not far from Gainsborough, you may like the farmer's market held at Neal's Yard Shopping Centre on the 2nd & 4th Saturday of every month. It's not massive, but what is there isn't too bad, plus the shopping centre's pretty good too.
If you're near Scunthorpe you may like the Pink Pig Farm, especially with the kids if you're an au pair. Also, the Old Farmhouse Pub / Restaurant in Scunthorpe's pretty good. Plus, they have a soft play barn attached to keep the kids occupied.