Beautiful city, nice and clean, quite and lovely people :-)
Make sure you go to Kings park and watch the sunset over the city and Rottnest island is a must,absolutly gorgeous! Its $69 for a return ferry ticket.
A good cheap hostel is Beatty lodge in Vincent street. Its $50 a night for a double or $33 a night for a single, dorms are also available.
Lots of restaurants in the city centre or in an area called Northbridge nearby, everything ranging from Maccy D's to italian, Korean, Japanese Greek

If you want a whole string of coffee shops and art galleries, get on the train and head to Fremantle. Its a hip place to eat and spend an evening.

I *love* this city! King's Park, the Mint, Gallery, Museum, Swan Brewery, the beaches, Hillary's, so many great things to do!

Must visit Little Creatures Brewery in Fremantle, just amazing place to hang out with your friends.
Great food.
Great beer.
;)

In Northbridge you can find a lots of asians restaurants also vegetarian restaurant, Italian Gelateria (ice cream shop) clubs and a lot more. Great night life and during the day once tired to go around you can relax in the park nearby. I loved that area very much.

Sunday session @ cottesloe beach hotel is well woth a visit if your into beach, sunset, girls, drink, beer...check it you

Try to rent a car for a day and drive down to Margareth River, enjoy some of the local wines, plenty of wineries,...

Go to the Kings Park for a Barbecue or a Pic-Nic. It's just perfect.

For seafood lovers, go to Freemantle and check out Kailis' for fresh items! See the seagulls too.

check out the Maritime Museums