I also second You Can't Take It With You and Lend Me A Tenor, my school did both, very funny!
We also did Harvey...I dunno, it seems like it shouldn't be for HS but I was production assistant...and we had sooo much fun in that show. It is quite long and needs to be shrunken, and might not have appealed to audiences so much but I really love it. Probably being biased, the two above prob are a little more appropriate for High school in terms of at least appeal.
"If there was a Mount Rushmore for Broadway scores, "West Side Story" would be front and center. It snaps, it crackles it pops! It surges with a roar, its energy and sheer life undiminished by the years" - NYPost reviewer Elisabeth Vincentelli