We usually try and let C adjust to local time when we travel - same as we do - otherwise you end up being up super early (or late) with nothing to do and being shattered in the evenings!
We've found C adjusts fairly easily when we're away now, we had a shocker coming back to NZ (5hr time difference) last year when he got sick but he still adjusted within a couple of days and when we got home he was great, 3 nights - 3 VERY early mornings and walks to the 24hr McD's for coffee for DH and I - and we were all back to normal