On average, the ship arrives around 7 AM and departs around 6 PM, it varies a lot. Some ports include an overnight stay, so you have plenty of time on Day One. There is a delay when entering a new country usually as they clear customs for the entire ship, so the boat can be docked while you wait a bit. Then there is whether the ship can dock or whether you need to tender into the city. Going inland requires a bus ride of course which can take hours out of the day.
I recall porting in Aqaba and the ship had our passports, we had a long tour of Petra and Wadi Rum and didn't get back until two hours after the ship was scheduled to leave, but they waited. I didn't want to be marooned in Jordan with no passport, I didn't even have photo ID with me that time. I got a bit stressed. I never know when they take up our passports, they didn't at all on this past cruise because it was all in the Schengen Zone, so no clearances needed.
I recall in Syracuse we got on land around 9 AM and came back to the ship aronud 3 PM. We walked over 5 miles, didn't have a "tour", just walked around.
Before we got to India, the ship took on a number of Indian Customs dudes, we saw them in the cafeteria dining. Then we cleared customs on the ship, but then had to do it again with each port of call, which was odd, to me, whatever, it was a fairly lengthy process at times. India is pretty weird overall I thought.