So, I was wondering if there was a way to have my phone act as a map while the computer runs the game at the same time. Anyone got any ideas?
Sure. This is essentially the same as a multiplayer game; you have an app running on the phone, and another app running on the desktop, and they communicate over the network.
Eon Altar does something similar that’s a nice twist on multiplayer RPGs. Each player’s mobile device acts as a controller to move the character and perform actions such as attacking, casting spells, and managing inventory. But the device also shows the player secret discoveries that other players shouldn’t know about, and it lets the player make certain choices without revealing them to the others.
I’ll plug a fellow local dev’s game Rollin’ while I’m at it. It’s kind of like multiplayer Marble Madness where each player’s mobile device is their controller.
Plugins like Easy WiFi Controller can give you a head start on implementing this kind of thing.