Gravity Rush Remastered features an auto-save system, but sometimes you’ll want to make a manual save of your own when you’re in between missions. To do this, simply head back to Kat’s hideout and you’ll see the option to save your game. You can get to Kat’s hideout by checking your map and setting a waypoint for the hideout. Alternatively, you can also look for the nearest manhole on the map, and use that to fast travel back to the hideout.
The manholes are used as fast travel warp points in the game, so be sure to activate them whenever you see them in town.
When you’re back at Kat’s hideout, you can also choose to warp to different manholes you’ve unlocked throughout Hekseville and change into the various costumes you’ve found in the game.