I grew up close to a par 3 course that also had an 18-hole mini golf setup. I played there multiple times before I ever owned a set of clubs. I loved going out there, even if I didn't really have any training on how to hit a golf ball.
I liked this setup, and while I like the idea of a large-scale putting green as suggested by Jim Urbina above, I frequently find myself becoming physically uncomfortable just putting for long periods of time - my putting stance seems to create the largest amount of pressure on my back. I'd also be concerned because, in my view, the easiest path to 'fun' for someone brand new to golf is get out there and whack the ball around.
Having said all that, as someone who already loves the game of golf, I would LOVE to see more or the large-scale putting greens in city parks or other central locales. I think I'd have a lot of fun with that, I just think it would be a harder sell to a non-golfer than, 'let's go down to the little par 3 for 9 holes'.