Thank you for all of the support. I try to think as an engineer... So here is my Occum's Razor (the simplest solution is usually the correct one) summary. Please confirm if my think is correct.

1. The Alternator or it's pulley is making noise first thing in the morning.
2. After warming up for about 15 minutes the noise disappears for the rest of the day.
3. I drained the battery some by leaving on the lights, with the engine off, for about 15 minutes. This would create an environment that would simulate a similar load that the alternator might have during startup first thing in the morning.

The noise returned.

My question:

1. How do I segregate out whether or not the noise is from the Alternator or from the pulley?
2. Should I replace the battery as well?

By the way I believe that I have found two potential candidates as a mechanic. I am just concerned that they will recommend an alternator rather than a pulley.

Thank you again for helping me think this through.

Peace,
Gino