I picked up a 99 Accord this weekend with 159K miles for a song. It was kinda dirty inside, but cleaned up real nice.
(Magic erasers and steam cleaner) and there's a little paint oxidation on the roof (black). It drives and shifts fine, and
seems to have good power. AC and and all windows roll up and down smoothly. I just got it as a daily work commuter.

There are two issues. One may be related to the other, but not sure.

First is vibration. It starts after the car warms up and drops to idle RPM. It intensifies when in gear or when A/C engages.
I know enough to know simple things to check first. So I checked (looked at) what appear to be the 3 easily visible motor
mounts in the front of the engine bay. Just looking at them, the rubber looks good. But I'm am amateur at best. If someone
tells me what's wrong I can usually fix it. But diagnosing is not my thing. I've also been told the rear/transmission ones don't
normally fail....(not sure how true that is, if at all).

I've also read that a bad or loose timing/balance belt can cause vibration, which brings me to the "whine" I hear. I posted a
video on youtube to hear the whine. I get even further perplexed when I read many people get timing belt whine after changing.
Some say it goes away after a few thousand miles, others say never. Some say it's normal, others say the tension isn't right.
There is no record the timing belt was ever changed, and the guy I bought it from was the second owner who had not done it
in the 9 months he owned it. He like myself assumed with it's mileage and age that it was done.

Anyway, here's the video of the whine.
I'm just concerned with the higher mileage (not really for it's age), that something sinister is about to go down. And even
though I got a good deal I don't want it to be a money pit by ignoring a problem.

 

Sounds like your belts. Unless something is seriously overdue for some lubrication.

 

Belts as in timing/balance or just the regular alternator/power steering, a/c?

 

Your PS belt is separate from your alternator/AC. It sounds like one of your accessory belts.

 

Yes, I was just trying to group them. The belts seem fine, none of them seems over tight. Ugh. Maybe a bad pulley or pulley bearing? I guess I'll go have it checked.

 

Sounds like a bad bearing.

 

Like in a main bearing or alt/compressor bearing?

 

Get a long screwdriver or broom handle, place one end of your new tool against the PS pump(not the pulley) and rev the engine while placing the other end against your ear/side of your head.
Does the PS pump make this noise?
Check teh A/C compressor, does it make this noise?

If someone put a heavy hydraulic or gear oil into the PS pump it would whine. ATF is what power steering systems take.