When the house was built, the trim carpenter had to hit the studs to nail in the baseboards, so that's where you look for stud locations. If the painters did a perfect job with the putty so that you can't see the nails (kudos to the painters) then get a magnet or better yet, a magnetic 'wiggle' type of stud-finder made for finding metal studs in commercial walls. Find one and 16" centers should work- if they don't then it's not hard to find them all this way one at a time. If you need the exact center, use a small finish nail (or drill for plaster) and probe into the wall where the top of the baseboard meets the wall downward. A dab of caulk (almost always white) will hide those holes well till the next time you paint.

Just another of my 'idiot-proof' methods for those of us like me who tend to forget that things don't always work as they are supposed to