We are thinking of staying within the pedestrian only Old City in Dubrovnik. Unfortunately, our flight leaves at 6:30 am so we would have to leave the apartment at about 4:30 am and walk with our luggage to the closest city gate where we would meet our taxi. Does anyone have a feeling for how safe that would be at that hour of the morning?

I wasn't out at that time of morning when I was there, but it seemed perfectly safe late at night. You might check with the apartment's owner. Some will pick you up and take you to the airport.

I assume this is to make a connection somewhere like Frankfurt. Would you consider flying to the connecting city the day before and spending the night in a soulless airport hotel?

If you have to meet the taxi, you will not sleep much the night before.

But it is perfectly safe.

We only have 2 nights in Dubrovnik on our own at the end of a tour. Our flight at 6:30 am stops at Zagreb and goes to Paris on Croatia air - we can't change it. We could stay outside of the Old City where a taxi could pick us up but we would really like to stay in the Old City.

We stayed in the Old City for four nights summer 2011 and while I wasn't up THAT early, I was up early (6am) most mornings and walking around by myself before anything was open and never felt at any risk.