I've been thinking about this because I may soon find myself in an apartment near important political and military targets. I would be most worried about fast shocking mass casualty terror attacks as the prime threat.
I would start with assembling the kit recommended at Ready.gov - Prepare. Plan. Stay Informed.
In case of CBW attack, I'm thinking that it will be important to have the duct tape, the plastic sheeting, and a way to turn off the air conditioning. I'd also like to have gas masks available. Then, I'd also like to accumulate a good 2-3week supply of water and food supplies.
My thought is that I'd want to shelter in place in the immediate aftermath of an attack and then to evacuate after a week or two of sheltering.
For small arms, I'm thinking that a typical high capacity pistol would be sufficient for self-defense (and retreat) in the face of an organized Mumbai-style terror attack. The government does not lack firepower where I might be moving.
I like Ineffable's approach of organizing neighbors. In our Atlanta complex, all the dog owners generally knew each other and could keep an eye on each others apartments and cars. Since we were walking the complex regularly, we were able to keep abreast of crime and other developments. My dog and I also discovered the scene of a burglary and were able to alert the police and complex management. The hard part was determining which neighbors to trust.