Hi Hcshi,
If you plan to climb KK, must remember to do some training, 5-10km run, stairs climbing with load... Actually I think that period is a wet season. So bring rain gear too! 8-))
If I am not wrong, Sutera Sanctuary dominates the lodging at Mt KK, so if you are climbing, you have to go book with them the accommodation. Visit their website for more details: http://www.suterasanctuarylodges.com.my/
And bookings usually have to be done half a year in advance!... or unless you join a trekking adventure group (there are some local ones like X-trekkers, SAC, BOAC etc).
For side trips, you can go visit Tunku Abdul Rahman Marine Park (it's made up of tiny islands)... for snorkeling, diving, R&R.... good place to go after climbing KK....(must go Poring Hotspring to reduce the muscle soreness after the climb too!)...
Well, that's what I did the last time (many many years ago... haha), so not sure if my info is still a popular choice... but what's important is you get to breath the fresh air and be away from our harsh envt for a while!