We are a young couple moving to Perth and need some suburb suggestions?

Not sure how long ago this was posted, but I'll respond anyway.
Depends a lot on price range. I currently live in Wembley, which is fairly close to UWA, and is one of the more affordable western suburbs. West Leederville is similar. Subiaco and Leederville are good for going out (resaurants, bars etc.), but are a little more expensive. Nedlands which is where UWA is may also be a good option. Anything in the western suburbs between the city and the beach tends to be pricy, but nice. If you are looking for something a bit cheaper Victoria Park and Maylands are some of the cheapest suburbs close to the city, and have good public transport to get to city/uni. I'd generally stay a little bit away from the train lines though as they tend to be higher crime areas (in my experience).

Also, look up the "circleroute" on the transperth website, good to stay on this bus route for getting to the main universities, shopping centres etc.