Which part of Rome is the best to stay for family?

Greetings, Our family is looking forward to discovering Rome in early June and would like to book an apartment. One site indicated accommodations are available in Trastevere. We are definitely a laid back family, NOT into any night life. What parts of Rome would be recommended to recharge batteries/ sore feet in a quiet part of Rome? Having markets close by would be nice. Should I proceed with Trastevere? Many thanks!