You can navigate the city by selecting the location in the Tokyo Access Map. There are certain locations with sub-areas. You can freely travel to these sub-areas even if you're already inside the main location. The game has no day/night cycle so you're free to do whatever you want and explore wherever you want without any time pressure.
Shibuya is your main hub in the game. This is where you can find the shops, vending machines, and other story-related spots. It's bustling with people and you even have to cross the road frequently to access all establishments in the area. You can walk or just use the Tokyo Access Map to fast-travel to the establishments.
Dungeons in the game are called Idolaspheres. These locations have fixed maps which you can view from the Gamepad. While you don't have access to the map from the main game screen, the maps stored in the game pad has sophisticated information that can be viewed anytime when you're playing the game.
Idolaspheres have several different navigation gimmicks but it's common to find multi-layered Idolaspheres, blocked paths, and portals. You can enter and leave Idolaspheres anytime you want. Since you can also save the game anywhere and one of your party members have the capability to teleport to the dungeon entrance, you can pretty much grind and resupply as often as you want.
In Idolaspheres, you can also interact with floating diamond item containers to loot its contents. There are certain containers that will require Treasure Keys. These keys can be obtained from other containers or as rewards from completing Requests.
Enemies appear as cloaked mirages that you can avoid deliberately or hit with your sword to stun them temporarily. Touching these cloaked figures will initiate combat. There are also special enemy symbols called Savage Mirages that can't be stunned by your sword. This enemy group is usually composed of powerful mirages so be careful when engaging with one.
There are also non-hostile mirages that you can talk to in dungeons. Some of them will provide hints for navigation while others may open up new Requests.