Specialized hardrock mountain bike would be a very good choice for a nearly bombproof ride. They have a model with disc brakes that i THINK will fit in your budget, if you ride in rain. Put some low lug height tires on it and you should be good for everything.
If you want more speed, take a look at the Specialized Crosstrail. Bigger 700c tires, that are fairly wide, and a suspension fork. You are gonna want a little cushion up front for potholes and curbs.
As and end note, if you have to leave it locked outside where theft is a possibility, then I agree with
exile that you should find an older less flashy mtb. Though there are some pretty good locks out there these days.
Good luck, i couldnt Imagine riding in a big city. Crazy. I will stick to my quiet country backroads
