Answer Me from The Band's Visit has literally brought me down from an anxiety attack before. I'm sure there are infinite more, but this was my first thought.
"You Walk With Me" from The Full Monty "Sleepy Man" from Robber Bridegroom "By My Side" or "On the Willows" from Godspell "They Were You" from The Fantasticks "Lazy Afternoon" from The Golden Apple
...and so many more, but I don't want to completely hijack this thread :)
"Seeing You" from Groundhog Day is the first thing that popped into my head. Also the finale of "Natasha, Pierre, and the Great Comet of 1812" is quite beautiful and peaceful.