It's hard to say, I suppose it depends quite heavily on personal preferences.
The one place we had the washer and dryer close to the bedrooms (2nd floor), it was just a closet. So, while it was true that it was close to where most of the clothes were generated/needed, we couldn't use the machines at night (noisy) and we had basically no space (just the hallway) to actually do laundry, so I didn't much care for it.
Another place the laundry room was near the kitchen, and it was also very small, barely any room for the ironing table besides the washer and dryer; it was convenient in that it was just a few steps from the kitchen, so we could keep an eye on things instead of climbing up and down to the second floor all the time.
The places I liked the most (and that includes our current home) the laundry room is in the basement. Lots of space to do what we need. If the basement is decent at all (finished floor, well lit), I think it's worth the bother of climbing stairs. Also, one can close the door if the noise/mess is too much and some visitors which don't appreciate laundry (the nerve!) show up. ;-) But if I had a choice of a large laundry room near the kitchen or in the basement, I'm not sure which one I'd pick.
