Basement laundry is an inconvenience in a two story home. For the person who does the laundry in an average family, it might be a discouragement. A second floor laundry room can be remodeled into a small space, such as a 24" linen closet between bedrooms, installing a stack washer and dryer.
The most difficult part of the project would be installation of feed and drain pipes to the basement. The dryer venting can be run through the ceiling and roof in a straight line. The use of PEX water lines makes the plumbing of a water source allot easier due to the flexibility and quick attach hardware of this product. When installing the drain system, include a drain-pan to prevent water damage in the event of a leak. Use pressure sensitive or electronically controlled valves to washer feed connections which detect pressure release and will shut off the source water.
The biggest issues will be how to run wire and pipe to the basement without tearing up the walls on the first floor. Depending on the location of the laundry and the existing structure, lines may have to run through the first floor ceiling and then through the top and bottom plates of a wall in order to reach the basement. To avoid exterior wall damage or removal, lines can be attached to the surface of a wall and then boxed in and pained to match existing. This is especially good if running through a wall means dealing with insulation.
Other locations for a small laundry on the second floor may be the master bedroom, a bathroom that is a bit more than average in breadth and width. It can also be placed in a small, unused bedroom or office and concealed behind a stained bi-fold door.