From what I know, you can't get to the Scholar District until after [spoiler], which you haven't gotten to yet.
Just take the train from Route 9 to GDC if you haven't already, then go north of Central Square to the Axis High courtyard, where if you haven't already, you will need to talk to Erin, go through some cutscenes, and have a battle with someone. Once you are finished at Axis High, go west to the District of Hope, then the hospital is just north of there. The bridge also opens up to connect the south side of District of Hope to Pokestar Studios, so you can take a shorter (I think) route back.