Lincolnshire is quite a varied county, and sufficiently varied depending on where exactly you're going.
Skegness (It's Bracing) on the water is completely different from Cleethorpes.
Grimsby different to Cleethorpes just around the corner.
The cathedral city of Lincoln (don't miss the Steep Hill) is dramatically different from Stamford with its many churches and beautiful buildings (my fav town in the ceremonial county, and its just down the road from me, and has the incredible Burghley House).
The fens in the south and centre are very different to anything in the US.
Market Rasen is an interesting place, and there are Lincolnshire suburbs of Hull.
The home of Isaac Newton (a descendent of his apple tree is near the house (National Trust) is near Grantham. Another great National Trust property just the other side of Grantham is Belton House with its several gardens and often village cricket on the lawn in front of the house. You won't be able to pack folding chairs in your car but I assure you that an afternoon watching the lads is good fun.
And then the World War II airfields and aviation museums.
The Hawks of the Red Arrows are based at an RAF field in Lincolnshire too....
so don't write off Lincolnshire.
If you say where you are heading we may be able to help details.
And yes, it is pretty flat.