You'll need to define ''not too far from the CBD'' .... for the average Australian, ''not too far'' could mean driving 45+ minutes...
As mentioned, it also depends whether you want to kite flat water or waves.
if you don't mind gusty winds but you prefer flat water whilst being within a 20 min drive to the city. think about staying close to the river in Perth (Applecross, Melville, Attadale).
if you prefer ocean kiting, waves and downwinders, think about Swanbourne, City Beach, Cottesloe or even Scarborough. Most of these are also about a 20 min drive to the city.
If good vibes, going out, nightlife, etc is what you're after, definitely consider Scarborough.
Have a look at our location guide to get familiar with the popular kite spots, pros and cons, etc.:
www.kitebud.com.au/locations/Also worth a read if it's your first time kiting in Perth:
www.kitebud.com.au/perths-kitesurfing-travellers-guide/