When you're hopping between time zones one of the first things you'll want to do upon arrival is fall asleep, but try to resist the urge.
Your body clock is likely to be a mess, but the longer you can keep yourself awake on the first night – aim for 10 or 11 p.m. – the quicker you will begin to acclimate to a new time zone. That walk is useful here, too, for keeping you away from the tempting lure of your bed.
Make sure you eat meals at the right times, even if you're not feeling that hungry, and keep yourself busy through the evening. That way when you eventually do go to bed you're less likely to be wide awake in the middle of the night.