The city recently completed The Green, a new putting course in Grant Park. I haven't seen the course yet, but it sounds like a mature version of mini-golf. You won't find any windmills, tiki torches, or mini Statues of Liberty (if you're looking for that, you can't do better than Par King, though Novelty Golf at Devon & Lincoln is my traditional favorite), just greens to putt on amid a landscaped garden. You also won't see any rabbits on the mini course other than the rabbit statue, a memorial to the 104 plant and flower eating bunnies the city evicted from the grounds.
I definitely want to make a visit to the park, but I'm going to wait until the throngs are gone this weekend.