if you are willing to put in a it of work you can grow your own green. When I moved into this house 2 years ago, the previous owners had a 600 sq ft garden that I converted it into a creeping bentgrass green. Finding a mower is the real tricky part, but its doable. It requires alot more work than synthetic, but its fun to be able to control the speed and hardness of the greens yourself. For instance during US Open week you dry it out and double cut it to make it fast and firm, or you can water it a bit more if you want to hit 50 yard shots that are more receptive.
http://www.kinipela.ca/green.html
Edit: My bro has a synthetic one and they are awesome for putting, really great.