I read somewhere on this site that the better the tire pressure, the better the mileage. My Goodyear Integrity tires say 44 psi, but my roommate said that might be too much. What is the optimal tire pressure for the Prius?
44 is fine, though the consensus seems to be that fronts and rears should have a 2 PSI differential due to the car's front end weight. In other words, 44 front, 42 rear. 44 is the maximum cold sidewall pressure (meaning first thing in the morning before driving) specified by Goodyear. And what you've heard about pressure's relationship to fuel mileage is correct: The higher the pressure, the lower the rolling resistance.
I prefer 40/38, its less of a bumpy ride. Try out different tire pressures, its whatever you are comfortable with.
44 front 42 rear is good. As you said, the higher the better up to the tyres rated limit. Check tyres cold. Maybe inflate a few PSI over 44psi at a petrol station on your way home somewhere close to home then let the tyres down to the required pressure when the tyres are cold. You will need a good tyre gauge but they are cheap. Use dial type rather than stick type.
As they've already said above, the front should always be 2 psi higher. People on PriusChat report tire pressures ranging from "factory installed" all the way up to "I don't want to scare you." At a Chicago Prius Group meeting, we sort of got a slap on the wrist for mentioning the idea of over-inflating tires for improved mileage. For that reason, we no longer promote the practice (publicly). But I can confirm, without self-incrimination, that 44 psi is just fine and within the tires' safety limit. Your roommate is nice and considerate to be concerned about your car and your safety. Take them out to lunch and enjoy that you have such a friend.
I'm running 45psi. "Don't tell me what it is designed to do. Tell me what it can do." The spec on the door is a negotiation between Toyota & Goodyear. The spec on the tire is Goodyear's opinion. Optimizing your fuel economy is not in their best interest. The longer the tires last, the less they sell.