The 2x4 sill-plate (bottom of a wall) is nailed to the sub-floor with nails that often go through the sill-plate thereby making them visible in the basement assuming your basement ceiling is unfinished). I've used this as a guideline for determining the position of a 1st-floor wall. Once I have a bearing on the wall's position, I go back to the 1st floor, remove the quarter-round molding and drill a small pilot hole (as suggested above) through the floor (try to avoid drilling at an angle). Insert a wire or coat-hangar, go back down and find its position. Now, on the basement ceiling, measure approximately 5-1/2" from the pilot hole and that's the width of your wall. Mark the center of the line and that should land well within the wall cavity.
4" for the internal 2x4 (it is actually narrower than 4") plus 1/2" x 2 for the two sheets of drywall plus another 1/2" (or so) for the baseboard (adapt that width for your wall thickness).
I used this technique to drill a 1-3/4" hole into the wall, from the basement, and landed smack dab in the center of the sill-plate (i.e. the hole-saw didn't chew out the drywall or moldings!). I needed a big hole in order to pass the AC power cable and serial connector for an ELO touchscreen.