|My thought was to get a better router (don't N's have greater coverage than G's?)|
That is appearing to be a common misconception on the part of some people. The difference between a G and an N wireless device is the bandwidth available to users connected to it. G is rated for about 56 Mbps and N 100+ Mbps.
Signal strength is dependant on the hardware. If the antenna is powerful, it will have better range. If the anntenna is weak, less range. I recently helped out a guy on here who bought a new N router that had a less powerful antenna than his older G router and he expected it to be more so because it was N.
Does this all make sense? Any specific router you'd recommend?
It all makes sense to me :)
I would say you're not likely to find a single wireless device that will provide adequate coverage throughout your entire home unless that device is centrally located inside your house. Have you tried locating your one wireless router in the center of your house to see if it provides adequate coverage?
If you want wireless N at both points, you'd need two wireless N devices. If your present devices are both G and you use one of them then devices connecting to it would only get G bandwidth.
As for recommendations....I have had excellent experiences with Linksys devices (now owned by Cisco company). I have no particular recommendations though at this point in time as I'm using an older WRT54GL at home and I don't believe they make and sell that particular model anymore.
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.