I think you'd have to build it yourself to keep the price at $2000. For that kind of range, you would want around 1,000 watt-hours of battery. If you want to cruise at 15 mph or so, and are in good shape, you could get by with less battery.
Let's say you need 200 watts to maintain 15 mph. If you are putting in 80, that leaves 120 watts for the motor. At 15 mph, it would take 6.67 hours to go 100 miles. 120 watts x 6.67 hours = 800 watt-hours. Accounting for some losses in efficiency getting from the battery through the controller and out of the motor adds in another 20%. Now, we are at 960 watt-hours.
There are bikes out there with that kind of capacity but none in the price range you want.