The exploration of game world in the Second Son, in comparison to the earlier installments, works in quite a different way, due to the fact that Delsin Rowe has a different array of skills from his predecessors. To make the journey more effective and convenient, the hero uses the power of smoke, which has been widely described in the "Step 6" section. I would especially recommend a regular usage of the power allowing you to turn into smoke, for it increases the process of movement, shortening the time needed to reach a given place in the process. Additionally, it allows you to phase through obstacles (barricades, metal gates, parked cars, etc.) or to get to a currently pursed person faster. Another advantage of travelling in this manner is that you won't be using any of your smoke reserves, meaning that this method can be used infinitely.
During your exploration of the Seattle, you don't have cling to the surface, especially that the game clearly encourages a more effective (and showy) course of action. A good idea is to bounce off of the nearby cars - doing so thrusts Delsin up in the air. Also, the main character is constantly encouraged to visit ledges located above the ground, as well as rooftops of the buildings. Despite the fact, that Delsin can climb them up in a traditional manner (by grabbing subsequent edges and interactive shelves), it's a rather arduous process, that makes reaching a roof of a building of a moderate height go into dozens of seconds. Instead, you can look around for red ventilation shafts, which you can enter after turning yourself into smoke (a sample shaft is shown on the screen above). Depending on the type of the shaft, Delsin will be transported on a higher ground or all the way to the roof, skipping the laborious process of climbing and taking care of not to lose your balance.
Getting on the rooftops, by using "normal" climbing method, or via ventilation shafts, has a number of advantages. Firstly, you can move around the city in this manner, while using the power to turn into smoke and to float above ground will help you to get to other rooftops. I would recommend to improve the former one, which will allow Delsin to use two jumps before he will have to land on a solid ground. Travelling through the rooftops allows you to shorten the amount of time need to reach a certain place immensely, because you won't have to look for a proper course around the streets or obstacles. What is more, it's a good way to avoid confrontation with a large number of D.U.P. soldiers, because most of them are stationed on the streets, only some of them can be found above the ground, on rooftops or on observation towers.
Rooftops aren't the only above-ground means of transport around the Seattle. I would recommend to pay attention to the railroad tracks, going through many of the districts of the city you will visit, as Delsin can jump on and travel along them. This method has two major drawbacks - the railroads limit the freedom of movement, and you have to watch out not to run into a subway wagon, which will result in falling of the rails.
As far as Delsin doesn't have to be worried about falling to the ground, even from high altitudes, he must, however, avoid getting into water at all cost, as he lacks the ability to swim. This is even more bothersome, as you will be spending a lot of time in a near vicinity of water reservoirs, for instance when exploring the docks or traveling between north and south parts of the city. You have to remember about it all the time, trying to carefully execute your moves and use powers available to you (especially the ability to float above ground) to avoid a sudden drop into water. Fortunately, contact with the water doesn't mean an instant death, but your character will be defenseless until you get back on solid ground. Additionally, it means losing some time, which can be precious, especially in those missions, in which the time is of the essence.
The virtual Seattle isn't an especially vast city, but despite that, the game tries to easy you with the navigation around the area. I would recommend to summon up the world map regularly (by pressing the OPTIONS button), especially given the fact, that there are places of interest (mission location and additional activities) marked on it. The city is divided into a dozen or so districts, and by hovering your cursor on any of them, you will be given specific information about it (who controls it at the moment, what secrets are yet to discover, etc.). Besides the world map, you should also pay attention to the indications of the mini-map, which is located in the bottom right corner of the screen. This solution is strengthened by the fact, that you can find various interactive places on the mini-map, which aren't marked on the global one (for instance, ventilation shaft entries marked with the orange).
Another worth noting information, is that in the inFamous: Second Son, there's also an option of quick travel, which can be done between districts. This can only be used on the districts, which have been reclaimed from the D.U.P. hands (more on this matter in the "Step 9" section in this guide) - you will be able to use it as soon as you seize control over at least 2 districts.