When you visit a new city or you have a very short amount of time in a city the best way for you to optimise your visit is to catch the Hop On Hop Off bus. These busses have specific routes designed to bring you to the best attractions of a city conveniently and efficiently. They usually have headphones with information about the history, the architecture, the hours and prices of the attraction you are about to visit. You can then decide if you are interested in getting off the bus and visit the attraction or stay on and move to the next one.
The busses are very comfortable, most of the time double decker and equipped with AC that is great in some of the hottest destination.
In very big cities, or cities with lot of attractions you will find a choice of different routs that you can pick from.
When you buy the ticket you will receive a map of the busses route, stops and frequency. In some cities you will be able to combine the bus fare with some or all the entrance fees for the attractions.
In my personal experience I used the Hop On Hop Off while visiting new ports on a cruise or if I had a very long layover in a new city. My personal preference is to do the all route once and then decide which stops I want to get off and visit.
Have a wonderful time in your new city!