Answer: RIGHT NOW! If you wish to grow broccoli for a fall crop, you need to be planting those seeds in the ground in the month of August at the latest. I planted my broccoli this month and I live in Michigan. Broccoli grows well in the fall, because it likes to grow in cooler temperature. It's also easier to do because a lot of your problems with starting it in the spring are gone. In the spring, the soil isn't warm, so germination takes longer. Also bugs are a greater problem in the spring/summer than the fall. Broccoli can withstand frost to a certain point. I plant to cover my fall broccoli whenever there is going to be a significant frost (under 30 degrees) and see how long I can keep it going.
If you haven't planted your broccoli yet and live in an area where the first frost is coming in early to mid October, I would look for a variety that you can harvest in the least amount of days. Just check the back of your package of seeds. Also the good thing about buying seeds now, if you can find a place still selling them they should be on clearance.
Click here to read about my experience growing the Packman variety of broccoli this year (I started it in the spring).