Depending on which uni you will be attending will make a big difference on where you want to be. I would not recommend Palm beach as it is a 40minute drive to Manly and then you would have another 30 minutes to get to the city centre. Palm beach is beautiful but a long way from anything else. Great if you are not working or work from home but is still a pain if you are planning on enjoying the nightlife in Sydney. Better areas closer to city but still North of city would be Mosman(cheaper then Manly where I live), Balgowlah or fairlight. Plus you may want to kite down at Botany Bay(not sure why any one would)and would be way to long a drive from North of Manly.
Go to Whereis.com and search for Manly NSW and look around.
Also best website for searching for apartments in NSW is domain.com.au
It lets you search by area, price, number of rooms even for places to share. You should know everything about your future place bythe time you are done with that site.
