"If we have to put a hole in the drywall so be it but the problem is where to do it?????"

The access hole goes where ever the transformer is. Finding said transformer may involve significant exploration.

"Does this definately mean the transformer is bad??"

No.

Bad? no.

Naughty? yes.

Such transformers by their very nature give off warmth and sometimes make that type of sound as a result of the "work" they do in changing the voltage. So I don't think it is necessarily bad. This transformer could operate for decades without a problem. However, if and when it goes, you are going to have to locate it. In addition, if it is plugged into a concealed junction box, then the installation was not done to code. It would also make me wonder whether the contractor had done more illegal wiring. Consider hiring another electrician to find the transformer and possibly investigate other wiring. This will involve some sheetrock damage.

"Such transformers by their very nature give off warmth and sometimes make that type of sound as a result of the "work" they do in changing the voltage."

It is a lower quality transformer if it is humming.

It means a lamination or cover is not tight.

You can tray and use the sound and a long screwdriver to find the transformer though.

Put the head of the scredriver against your ear and touch the tip to the ceiling.
Keep looking around to find were the sound is loudest and cut a hole there.

If you are lucky the transformer may be right there (or at least close).

If you have a mechanic's stethoscope it is easier and faster.

I'll second Brickeyee; go to an auto parts store and get a mechanic's stethoscope. This sort of looks like a doctor's stethoscope, except that instead of the little thing that the doctor puts on your chest, it has a long metal rod attached. You touch the tip of the rod to the place you want to listen to. Mechanics use it for pinpointing noises inside of car engines. Go around the room touching it to the ceiling in various places, and you should be able to pinpoint where the transformer is.

Thanks for the suggestion -- I have never heard of a mechanics stethoscope. I was hoping to borrow a friend's real stethoscope this week when she is not at work. Will update as soon as I get my hands on the scope.

Will a circuit toner signal be attenuated by a transformer? If so, would turning off the power and attaching the toner to the doorbell leads help locate the transformer?

Before ripping into any drywall, why not check all accessible junction boxes first? Often (not always), the transformer is not given its own box and just attached to a box that is close to the door switch-bell line. That box should still be accessible and you should be able to tell the one that has the transformer by looking from inside the box.

BTW, this is the exact reason that before drywall is installed, I take extensive pictures including closeups of any junction box. Each picture covers around a 4' x 10' section, with closeups being as close in as possible to have the junction box (and incoming wires) fill the field of view.

"Will a circuit toner signal be attenuated by a transformer?"

Yes. The transformer is optimized to operate at 60 Hz and the higher frequency of the toner will be greatly attenuated.

"If so, would turning off the power and attaching the toner to the doorbell leads help locate the transformer?"

Only if you have a unit that supplies its own power.
The typical AC power units for locating breakers use the power to operate the sender.
Communications systems locators normally have their own battery power, but often cannot tolerate the presence of 120 V AC on the wires.

There are a few power line systems that have their own power source and can operate on either live or dead AC wires.

I have one of those kits that has a battery powered tone generator with twin alligator clip leads and a separate amplifier probe. I have to make sure there is no voltage present when using it.

Being able to trace a wire in-wall has saved me many times.

I also have one of the plug-in outlet testers that lets you determine which breaker is the one powering the outlet. The tone generator runs off of AC power, which is helpful since the probe doesn't always point you to one breaker. Shut off the wrong breaker and the chirping remains. When you shut off the correct breaker, the chirping stops.

Our contractor arrived this am and with the help of a medical stethoscope -- we were able to locate the transformer without about 5 inches. We cut a hole in the ceiling and put one of those plastic access panels there so there is no drywall repair.

The transformer was actually just loose and vibrating. Tightened it up and there is no more buzzing!!!

This was certainly a lesson learned.

Thank goodness for the internet -- I learned more about doorbells then I ever wanted to know.