Apartment brokers/realtors aren't a thing here.

Since you're moving for grad school at CMU, I'd recommend looking at Oakland, Squirrel Hill, Homewood, Point Breeze, Shadyside, and the Regent Square area (it's a mix of Swissvale, Wilkinsburg and Edgewood). If you don't have a car, these neighborhoods have bus lines that right by CMU or within a block in these neighborhoods. Even if you have a car, parking at CMU can be expensive so it may be worth it to plan on bussing to/from campus.

August is a popular move-in month because of students coming in, vacancies start popping up now - June. Depending on how particular you are, what you look for in an apartment (must haves vs nice to haves), you can start looking now.