make up your own story, seriously. This book in the AP has little story, just build up the adventure, have factions back stab, I personally took the human district and turned into a base of operations and had quite a bit of story happen there between the "leader" of the human district and basically gave them missions to other districts. I scrapped the camp site system and am just going to have encounters between districts and factions.
I always like to look at communities and imagine what their day-to-day life is like. In particular, do they have sufficient access to food that they might have some sort of leisure life (such as sports)? Even if they don't, there might be a local pub where they meet after a long day. Do they have any sort of trade at all with other groups? Do traders ever stay overnight? If so, who puts them up. Who makes their clothes/weapons/equipment, and out of what?
Once you've answered these questions you'll probably have at least a half dozen new NPCs with roles other than "fight people who aren't us". It might even springboard you into story.
Need a concrete example?
If your players want a sandbox CoSS delivers that out of the box. You might want to play along with the players' actions, just setup the situation and see how they handle encounter with rival factions; let them do the work and react to their actions with the tools the module already hands you. It works great for my game, hope it might help you as well.
Also, gather together all the set encounters...that's your sandbox. Don't worry about them being slightly out of whack...the PC's can take each at their own pace, including scouting, preparing, and so forth. If they can nova an encounter site, they can hit waaay above their weight.
You can play all the politics you want to, do as they like, there are tons of rote enemies to be slaughtered and you can throw in endless amounts of random encounters from the jungle beyond. Use the camp/research etc as points of progress/security/influence over the city. Foiling the growth of adversaries should be great to play as they solidify their power and influence over the city.
Just make sure you don't put in the vaults until it's time for them to start going down to the city below.
And they are going to need some serious power to do overcome the challenges of the Gorilla King.
As a thought...if they never activate the golden spears (and really, why do they need to? they've got a teleport chamber! And high level spellcasters can totally close the stairs heading to the deeper levels) they get to keep the magical effects of the city active for perpetuity. I know that I would be totally loathe to give up that magic if I had any choice in the matter.
==Aelryinth