Overwintering Lemon Grass Indoors

I purchased lemon grass this spring and noticed it is a tender perennial. I would like to keep it and wondered if it would be better to keep it in the basement which has one window and is fairly cool, in the cold room which is darker and cooler or upstairs in my house which is quite bright but very warm. I also wondered what zone it would be.

Both Cymbopogon citratus and Cymbopogon flexuosa are rated for Zone 11 and higher, which means that they cannot tolerate any frost.
I think the best place in your house would be upstairs because any area with too little light would mean that the plant would have lost too much strength by spring due to too low light conditions. Try not to have it right over a radiator if at all possible and maybe try to keep it a bit cooler by moving it closer to the windowpane. Keeping it cooler in the winter will help the plant cope with lower light levels.