As a new Leaf owner, I have several points of advice... First, like all rechargeable batteries, the battery has a limited number of charge/ recharge cycles in its lifetime. You SHOULD NOT be experimenting how far you can drive before the battery cuts out. When you discharge a battery down to 0%, that is not good for it. You should regularly try to charge the battery before it reaches 20% charge, and preferably closer to 30%.
DONOT used the estimated "miles of range" as any indication of how far you can drive. The battery "% of charge" display is the best gauge to measure by. Figure that with your battery, every % of charge will give you about 1 mile of range (maybe a bit lower).
Also the estimates on the dashboard of how long it takes to charge with the factory charger is worthless... Consider that the 120 volt charger will charge the car at about 5% of charge PER HOUR.... So if your car is showing a "50%" charge, it will take about 10 hours with that charge to reach 100% charge... Good luck with your new car....