Hi Dave.
Is it a slow ballad? Maybe "the Second Time Around." I have a compilation with some tunes very similar to those on the record you're talking about, and the tune labeled "April In Paris" is actually "The Second Time Around" and the tune labeled "The Best Things For You" is actually "April in Paris."
On this version of the compilation
http://www.amazon.com/Cross-Country-...9296824#disc_1
The track names seem to be all corrected.
That version of April In Paris is great, with some classic Israel Crosby, one of my biggest influences to be sure. Of course, you've already had a listen to Basie's famous version, right? I don't think you can play the tune in an informed way without being familiar with that version.
If you like The Second Time Around, it's a Jimmy Van Heusen tune made popular by Sinatra.
Brent