If you're looking for a good cardio workout, cycling is one of the best - if not the best. But, you shouldn't worry so much about miles as you should about time, and quality.
You should expet to ride approximately 20-30 minutes at a good pace, say a cadence of between 75 and 95 (big range, but it depends on your fitness level) - and that's not really difficult to accomplish. When it's all said and done, you'll have ridden approximately 10 miles.
As your fitness level increases, you can increase time, which will increase distance.
There is no set mileage you should ride.
Also, though - if you do ride like this, be sure to have seat pack with an extra innertube and tire/tube changing tools, an air cartridge or two, and an air cartridge tool to use the cartridges. You'll thank me the first flat you get on the road.
Good luck!!