John Quincy Adams went on to become a Representative for MA in the House and I'd argue was the only real demotion post-presidency.
William Taft went to the Supreme Court after his Presidency (not exactly a lateral move in and of itself) but was the Chief Justice so it's probably close. Then again institutions powers wax and wane over time, so it could be argued that it was a demotion.
Lastly, kind of a bonus factoid of post-presidency activity -- Teddy Roosevelt, after serving a term plus some (edit: he took over the presidency as the VP after McKinley's assassination) and was a Republican. He later ran in 1912 as a candidate for the Bull-Moose Party after a rift in the Republican party when they nominated the above W. Taft instead of himself or another more Progressive Republican.
How is SC seat a demotion? The only real power the president has is wartime, and Americans aren't fond of war especially if it has a chance to end up at their borders.
In addition to the veto power mentioned above, there's also the power to issue executive orders and to nominate judges, including supreme justices. Those are fairly significant. There's also the influence they have over foreign policy.