Okay, first, I wouldn't worry too much about getting caught in a terrorist attack. Not much you can do about that but relocate.

A vehicle is a tool. Maintaining the tools we use and rely on is a survival necessity. Keep your car in good running order, and you minimize the risks.

Urban EDC ought to include the following, though this is by no means a thorough or complete list:

A spare stash of cash
A good multi tool (not considered a weapon unless going through an airport, depot, or other such public transportation portal)
A pocket sized first aid kit
Various small useful items (safety pins, dental floss, duct tape, etc)
flashlight

It takes time to develop the appropriate edc for your needs. Each of us has a unique combination of daily needs, so the list really depends on what you do and your knowledge of what you might need for any given situation you might face vs. what you are willing to pack around with you.

For instance, I pack 40 lbs of body armor daily as part of my EDC, but that is here. I am not likely to tote that around back home much. The bottom line is don't expect any quick and universal answer for what you should carry with you. The best suggestion is to take the time and effort to research it, ask pertinent questions of others (you are already on a good start just by being here in the forum), and then making some important decisions about comfort, budget, and contingency.

Good luck. Feel free to ask all sorts of questions. Lots of product review, Macgyverisms, and just plain good sense amongst this group. We are all in the process of learning how to do it better.