If my personal experience of owning the Whyte Coniston is anything to go by, the answer to 'how far can I go with an electric bike?' is: Pretty much as far as you need.
I commute 11 miles to work on my electric bike and it uses about 20% battery or less, on full power. That means I only have to re-charge every 4 or 5 journeys. Based on my experience, I should be able to go 55 miles on full power before I have to stop and recharge. A full charge currently takes me about 2 hours.
If you're going through battery faster than you anticipated, you can switch down to a lower power output, which is less fun but still keeps you going without much effort. I've only had to switch down to 'Eco' mode once and in 15 minutes of cycling I didn't lose a single percentage of battery.
Here's a great infographic on the topic by Giant: