Update

I replaced all engine mounts (except for rear engine mount) and insulators in my 2000 Civic, and both insulators in my 1997 Civic.

Vendor
All mounts and insulators were purchased from Majestic Honda.

Findings
2000 Civic -- Both insulators were basically destroyed (top row, left and middle in picture) and the left motor mount (top row, right in picture) near the timing belt had a gaping crack in the rubber that allowed the fluid contained inside to leak out. The transmission mount seemed fine.

1997 Civic -- The left insulator was destroyed (bottom row of picture), but the right one was fine.

Outcome of job
2000 Civic -- All vibration in the cabin and steering wheel is greatly reduced with and without the A/C running, and the exhaust system rattling noise is gone.

1997 Civic -- The vibration at the steering wheel when the A/C is running is gone.

Summary
Overall, the job was surprisingly easy. (I know the rear mount will be more work.) This job was well worth the time and money.

 

I do not know about Hondas with autos, but general motors and chrysler cars with autos have a "torque converter lockout switch". When this switch goes bad, you get a vibration at idle in gear (because it is trying to 'lock' the converter). The temporary 'fix' for this is to unplug it (but the converter won't be fully locked at hwy speeds so gas mileage will suffer).
To make sure you have bad motor mounts pop the hood and have someone sit in the car while running and shift it between gears - if you 'see' the motor jump when going from neutral to drive or from park to reverse then you definitely have a bad motor mount, and if you see VERY small movement then the mounts are fine.

 

Thanks for the input. I can't do your motor mounts tests now as I have already replaced the mounts and/or insulators.

The information about the AT lockout switch is interesting. Does anyone know whether or not this also pertains to Honda Civics?

 

So now that you've replaced the mounts is the vibration gone?
Here is the switch/solenoid I mentioned above for a 2000 EX AT
28300-P24-J01 SOLENOID ASSY., LOCK-UP (KEIHIN) $173.80
I do not know if there is a switch/sensor for this part or if the solenoid assy itself is what could be bad.
Your filter might just be clogged?
28320-P24-J01 FILTER ASSY., LOCK-UP SOLENOID(KEIHIN) $17.05
http://www.slhondaparts.com/browse.a...talogId=13S020