It appears the leak is coming from the bathroom sink and is leaking into the closet downstairs. There's a huge circle and it appears the problem has been there for a long time before I bought the condo. I've noticed that at times when the water is running in the sink, I can hear drops onto a hard surface so I'm inclined to think the leak is coming from the sink which is encased with a dark cherry wood unit with a marble top. How would one go about getting to the leak without causing major costly repairs? The ceiling will definitely need fixing (probably cutting and replacing the deteriorated section).

If you can see no moisture around the trap or in the cabinet then the leak is inside the wall in the horizontal drain line. This can be reached one of two ways.
1) pull the vanity and open up the wall,**OR**
2) Open up the wall on the other side.
I'd go with door #2 myself. Patching and painting the wall's a lot easier then tearing up up your vanity.
If the drain's anything but plastic replace with PVC. Good luck, Tom

Do you own or rent this condo and is there a home owners association with covenants and rules?

If you know you have to pull off and replace the wet drywall anyway, I'd start with pulling that off and seeing if you get lucky enough to see the leak. If so, then no extra harm done since you were going to repair that drywall anyway. If you don't see the source of the leak, then I'd do as Tom suggested above. Also, if you rent the condo, you'd best leave this up to the landlord to fix. That's the easiest approach!