Linksys has some "signal boosters" which piggyback on top of some of their models.
But....honestly I've heard of mixed results with these. Never used one myself.
First thing you can try....yeah, get that router upstairs out of the basement....you want centralized height. Wireless can be very finicky...it's all about what environment it's in. Different buildings have different results when it comes to wireless performance. Just keep moving it around, here, there, test it in every place you can. Moving those antennas around can make a difference.
There are some 3rd party hardware out there that makes customized booster antennas for Linky products also.
If wireless is a must in your house, you may want to try Buffalo Tech, they have some good wireless repeater projects...one base station...which can have several repeaters...say one on each floor, opposite ends of the building, etc.
I'm about to do a 1 story school with it. Haven't worked with their product yet...but my first contact with their tech/sales was very favorable, I'm looking forward to trying their stuff.