Hiya,
Here are some nice suburbs which aren't too far from Subiaco.
Victoria Park - this is just south of Perth city and would take roughly 25mins to drive into Subiaco. I lived here when I used to live in Perth and we bought a house here in September which we're currently renting out. Lovely suburb, near the river and the Burswood...very safe, good schools, nice houses, convenient.
Riverton
Shelley
Rossmoyne
Manning
Kensington
Como
South Perth
Dianella
Inglewood
Karawara
Burswood
Laithlain
These are other suburbs that I would recommend....most are south of the river (because this is the area I'm most familiar with, and they are all pretty reasonably priced for housing)
If you want me to recommend nicer suburbs which are a bit pricier...these are good, but it really depends on your budget -
Floreat
City Beach
Wembley
Claremont
Cottesloe
Dalkeith
These are all beautiful suburbs, houses are a bit pricier though.
Here are some websites to use for selling/renting houses in Perth.
Real Estate, Property, Land and Homes for Sale, lease and rent - realestate.com.au
Real Estate Institute of WA - Perth Property, Land & Homes For Sale or Rent in Western Australia
Real Estate for Sale, Rent and Share @ Domain.com.au
Good luck.
Gem