(Living in a major city)

I'd tell my girlfriend to stay put in our apartment and to make sure we have a lot of water reserves (before it's too late?). I myself would run outside with a few empty backpacks and head to the nearest grocery store (we have 4 of them within a .5 miles of our apartment). From there, I'd grab as much food as possible. I'd like to say that I'd pick stuff that can last then longest, but I probably wouldn't have the time to logically pick out the "best" stuff.

I'd then run back home and depending on the amount of time left:
1. Go back down and pick up more food and supplies (if there's time)
2. Barricade the front door (which really is the only access point to our apartment. We have no fire escape from the balcony and no neighbors can come on our balcony without seriously risking their own asses.

From there... Play monopoly?