"Bars" don't really mean a whole lot. Interference could be sporadic.
No, a gigabit router would probably not help unless there's something seriously wrong with your current router - in that case, replacing it with any new router would have the same effect. Gigabit is just for the ethernet ports. You're limited by the wireless connection, so it won't help at all.
A 5GHz Wireless-N router may help if the issue is congestion/interference.
You can use inSSIDer to search for nearby wireless networks. It will show you which channels they're on and their relative signal strengths. If there are a lot of wireless routers on the same channels you're trying to use, the throughput will suffer.
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