Regarding affordable, it all depends on your budget. $5000 is affordable for one person but might be out of reach for many others. In one area of the city, you might find a one BR for $3000 but in another location you might only be able to get a studio at that price. So try to figure out what you really must have in your new home. You'll probably end up compromising on something like we all do.
As far as safety goes its always best to live in a 24 hour Doorman building. That notion also brings up cost, as Doorman buildings tend to be the most expensive. In NYC though you have to show 40 x's the rent in income and have good credit. (If not, you will be paying extra security).
Give me a call to discuss some more.