Is there a tool to find a the closest spot on the other side of a wall?
The most common technique (other than careful measuring and mapping) is to drill a very small pilot hole through the flooring alongside the baseboard. The hole can be less than 1/8 and you can run a straightened clothes hanger through the hole to find it in the basement.

The hole would probably be behind or under the appliance, if the location were good, or it could be filled with wood putty or something similar if it shows.