In almost all situations when in a big foreign city, once you’ve checked into your hotel, you can then start roaming the streets without your passport. Be sure to lock it and other important legal documents in your hotel room safe or at the front desk safe, and leave it there until you check out. The number one way to ruin any travel experience is to lose your passport. You don’t need it on the street, and no one will steal nor pickpocket it from the hotel safe.