2 days in St Moritz what to do

Hi

I will be 2 days in St Moritz on 8th and 9th June. We are a family of 4 with 2 young adults.

I'll spend the 1st day after arriving from Zurich exploring the town and the lake. However, I would like to get suggestions to spend the second full day well.

I'll also be 3 days in Zermatt, 5 days at Wengen and 2 days at Lucerne after.

Hence, please let me know suggestions on what to do for that 1 full day St Mortitz. Thank you.