Safety Bay for flat water, further out than Woodman's Point though. (watch wind direction at Woodies to determine which of 3 spots to kite on - 1 is flat, the other 2 are small chop)
Use
www.transperth.wa.gov.au/ to look up public transport options
Re. backpackers hostels, the ones we tried in Fremantle were relatively expensive and horrible!
Maybe Scarborough is better?
Otherwise, I recommend
perth.gumtree.com.au/ for finding a room in shared house instead (search under short term). Cheaper and nicer but might be a challenge to organise before you get here.
We'll be gone by Feb but enjoy, many decent kite spots here as you can see from Location Guide on www.waksa.com