At first in any new city I look for Tourist Information Center. Usually you can get there a map of the central part of the city for free, with a list of all sights. This map is my minimum program that I need to complete in a new city. I use Google Map too, of course.
Because most of the sights are located in the city center, I walk a lot and use public transport only when there is an urgent need (for example, if one of the sights is far away, and it is important for me to see it).
Determine from the very beginning for whom you want to explore a new city - for your friends/relatives/your Instagram followers or for yourself. Because it affects the depth of your immersion into the city atmosphere: the desire to see it only through a camera lens, as for me, will deprive you of the moment and distract you from the point. My top tip: for quality research, clear your mind from unnecessary thoughts, don't photograph everything in a row (just what struck you most), engage all your senses and open yourself to new experience.
Look carefully at all houses you pass by. Pay attention to windows and doors (The same or different? Big or small? Old or new?), decorative elements, colors, building materials, the interaction of people with buildings (Are air conditioners installed on homes? Do people put their things on balconies? What are the colors of the curtains in the windows? How do the yards near the houses look like?) Analyze what is in common and different between buildings which are located on the same street/quarter/area, google the history of the building which impressed you the most. Consider how the architecture in this city differs from the architecture in your city.
Graffiti and street art
How city interacts with residents through visuals (commercial/political/social ads, slogans, sanctioned street art) and how they respond to it (graffiti, unauthorized street art) can say a lot about it. Pay attention to the drawings on the walls, city lights, bigboards, signs, murals, inscriptions. What do they have in common? Consider how graffiti and street art in this city differ from graffiti and street art in your city.
Pay attention to the topic that prevails in the sculpture of the city: whether they are monuments to prominent figures, whether they are samples of contemporary art, whether these sculptures are old or the majority of them are new. They may be united by a common topic/story/legend/style. Consider how sculptures in this city differ from sculptures in your city.
Look at the local people: how they are dressed, how they look, how they interact with each other, where they go, how they speak, how many men/women/children/old/young are among them. Try to contact them and look how they will respond to you. Remember that each city is created by its inhabitants, so who they are can tell a lot about it.
Consider whether this city is convenient for local residents. Is it convenient for tourists/people with disabilities/people with children/youth/seniors, etc.? What kind of transportation is there in the city, what does it look like, how much does it cost, how often it goes, how stops are arranged? How many malls/shops/markets/cafes/bars/restaurants/clubs are there, where are they located? How do the roads look like? How do traffic lights work? Are pedestrian crossings sufficient? Are there street signs everywhere? Where are the schools, hospitals, libraries, banks, government agencies, universities, how do they look like? Are there ports, exhibition centers, large/medium-sized manufacturing facilities in the city? Consider how the infrastructure in this city differs from the infrastructure in your city.
Each city has its own special voice. Listen to it more carefully: the sounds of transport, conversations of passers-by, birds singing, the roar of construction etc. You can even close your eyes briefly to listen to this voice. Compare how the voice of this city is different from the voice of your city.
Each city has its own special odor. For example, a port city can smell like the sea, a big industrial city - like plant emissions, a small town in the mountains - like grasses etc. Just listen to these feelings. Consider how the odor of new city differs from the odor of your city.