And 'without farmers' is precisely how I introduce Carcassonne to new people. You have to be pretty good at spatial reasoning to understand farmers and their fields in the game just from someone describing it to you. But most people get it right away (after the first game) when I say, "we'll play one game without farmers, and then look at the finished board so you can see where the fields and their borders are."
Of course, that only works for a game like Carcassonne which plays in 45min or less on the first go and can get down to 20min if you're playing with people who know the (base) game well.