|First, out of curiosity why wouldn't the N give better reception than the G? Isn't it touted to be an upgrade?|
How far, and how well, a wireless signal travels has nothing to do with the revision of wireless (A, B, G, N etc) and has everything to do with the power of the antenna. As you've discovered, just because a device is a newer revision, doesn't mean it's more powerful.
N improves bandwidth and gives 100+ Mbps bandwidth, whereas with G you only get about 56 Mbps.
Antenna power is a hardware issue unrelated to the actual bandwidth capabilities of a wireless device.
So this question applies to your suggestion as well. How would I make that 2nd router in a central location.
You're correct, your first router (Router 1) needs to be physically connected to your modem. As to how to located Router 2 in a central location....I explained that above. You would first of course configure it, but once configured, you simply set it in a central location and plug it in.
You would configure it to connect wirelessly using bridge mode to Router 1.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.