My spots of choice (riding a twintip not a surfie though) in Albany are Middleton Beach up the northern end away from the crowds, and northern half of Goode beach in the gorgeous flat water shallows! Neither of these spots are any good in a westerly though and i never found a spot that was good.
Also, i wasn't game enough to fly in the main Albany bay area but i'd imagine that would've been pretty damn sweet for flat water riding.

look for kites at the Princess Royal Sailing club. that is the place of choice in a SE if you want flat water and thats where all the locals will be. note, the commodore of the club will probably give you a hard time if he walks his dog down there and you dont have a membership. cranky old bugger.

other than that, middelton is okay for waves, simular to scarborough, but with a more gradual sea floor gradient. needs SE too.

if you get caught with a SW. drive towards camp quaranup and look for the small gravel driveway to the bay there on the left. great flat water, thight deep for as long as you could ever want, but can be quite gusty.

for waves in a sw go to mutton bird island, bit of a drive to get there, but the waves are nice and powerful if the swell is good.

Have fun.