eBike for NYC Commuting

Currently I commute by subway from Brooklyn to Manhattan daily. I am looking to buy an eBike to use for all non-rainy days. The ride is about 6.5 miles each way in stop-and-go city traffic (have to stop at all red lights in NYC). The ride is mostly flat except for the bridge which is maybe about a half mile long. I need a bike which will allow me to do this ride in summer (up to 90-100 Degree Fahrenheit) without breaking a sweat. On the ride home I don't mind pedaling the whole way because I can shower when I get home. So the bike needs a 6.5 mile range without pedaling (keeping in mind lots of stops and starts). The streets in NYC have a lot of bumps and potholes so a bike with some sort of suspension would be nice. I also need it to be either light enough to carry up to my second floor apartment, or a bike which can survive being stored outdoors in the rain. At work, there is a bike storage room on the first floor but I'd like to be bring the battery inside to charge during the day. Being my first eBike, I'm not looking to spend a lot of money. Two options I am looking at are the Cyclamatic Power Plus CX1 ($600 on Amazon) and the Electron Wheel ($800 at Best Buy) to convert my existing road bike to an eBike. I also wouldn't mind getting a kit such as the ones from Aosom. Would either of these fit my needs? Can you recommend other options? Any other NYC eBike commuters on here who can comment?

Summary of requirements:
6.5 city miles range without pedaling
comfortable to ride on bumpy NYC streets
light enough to bring up stairs, or storable outdoors
need to be able to detach the battery and bring inside to charge
 
I don't care for those all-in-one wheel kits. Too much to go wrong in one basket. No upgrade path when battery craps out. Kind of weak in power too. And almost everything I've used with my Android has been somewhat problematic. The last thing I want is my phone running my bike.

On the other hand, I see all those occasional gloating twitters from NYPD where they rounded up 200 ebikes. passed out $200 tickets and look to have the bike crushing party at the scrapyard. Is it safe to ride an ebike in NYC?

Read the reviews on the Amazon product. It's your basic $400 chinese ebike imported to USA and sold on a tight margin. I think it's OK, but but what might happen is you get a dud with a bad connector or something and it won't power up. If I got one, I'd just fix it, but cannot expect customer to do that. Then you have to worry about the quality of the battery, etc.

There's a shop called Propel, I believe, in Brooklyn, which has waged a legal battle to make ebikes legal in NYC. You ought to kick your budget up 2X and go talk to them.
http://propelbikes.com/
 
Thanks for the suggestions. Part of my motivation for not spending a lot is if the bike gets stolen or confiscated, I haven't lost as much. Also, it takes less time to pay for itself, when compared to a monthly metro card ($120). If I spend $600 on an ebike that dies in 5 months but I avoid taking the subway, I'm no worse off monetarily, but I will have gotten exercise.
 
Aren't Ebikes illegal in NYC? I see pics all the time of cops confiscating ebikes.

If you do buy one get one that doesn't look like an ebike at all. Your needs are pretty simple... I'd suggest a stealthy and light folding bike
 
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