Where should I mount a mirror? What do you recommend as an optimal point and orientation for mounting a rear-view mirror? I'm open to handlebar-, glasses-, or helmet-mounted.

Some of the considerations, as I understand it, are:


Ease of mounting.
View provided.
Vibration.
Likelihood of breaking.
Robustness for repeated off and on (for glasses-mounted).


I've got a hybrid bike with flat handlebars.

I'd also welcome specific product recommendations and recommendations about other aspects to look for in a mirror.
A mirror is a great addition to a cyclist's toolkit. While all cyclists should be able to look around behind them without one, a mirror lets you do this more often and safely. And a mirror is no substitute for looking behind you anyway. Here's a summary of the kinds of mirrors I've used. 

Glasses-mounted mirrors like the take-a-look mirror are great for giving you a wide, easily adjustable field of view. Pivoting your head means you can "sweep" the area behind you, and the mirror is close to your eye so it's a fairly wide field of view. However, they're only usable if you wear glasses or goggles, and some mirrors won't mount to some glasses, particularly glasses with thicker temples like some non-prescription sunglasses. 

I find that the take-a-look is a great mirror, but it tends to pull my glasses off just a bit over time. Adjusting it is merely an annoyance that I've decided to live with, since the mirror is otherwise excellent. (My glasses are also extremely light, and this would happen with any mirror, although the take-a-look is fairly heavy for a mirror.) 


Upside: Great field of view, keeps the mirror off the bike. Inexpensive. 
Downside: A little more finicky to adjust than bar-mounted mirrors, easy to forget. 


If you don't wear glasses, or prefer not to put a mirror there, you can get a helmet-mounted mirror instead. Most of these attach to your helmet with adhesive pads. The only one I've had that I cared for attached to a helmet's visor that was designed to accept it. Look at helmets specifically for commuters if you want one of these, I loved it but had to get rid of it when I replaced the helmet. 


Upside: The mirror is always there. 
Downsides: More vibration, smaller mirror, and you're locked into that helmet if you want to keep the mirror. Harder to adjust than any other kind of mirror, since your head is always moving and your helmet moves a bit on your head - unless your helmet is really tight. 


Handlebar-mounted mirrors are generally larger in area and have a curved surface. (Think "objects in mirror are closet than they appear".) The ones meant for drop bars usually mount with velcro or another attachment system, and the ones for flat bars will generally be screwed onto the side of the bars. I've never found one I liked for drop bars, but the flat-bar mirrors work quite well. 


Upside: The mirror is always there, and the permanently mounted ones are easier to adjust than any other system. 
Downside: A little clunky, they make your bike wider (an issue if you need to take your bike on the train or if you have a folding bike), and you need to look down to see it, taking your eyes off the road. Can be snapped off if the bike falls or grazes a wall. (Some are advertised as "folding on impact", though.) 


Recommendations

Outside of the ubiquitous take-a-look mirror, it's difficult to give specific product recommendations. But there are only a few kinds of mirror available, and even the most expensive mirrors are still fairy cheap. 

I'd avoid plastic eyeglass-mounted mirrors, as they tend to break. But a good eyeglass mirror will give you the best rear visibility. 

If you want to avoid eyeglass mirrors: In your situation, with flat bars, I recommend a mirror that screws into the sides of the bars. You can put on one or two mirrors, depending on your situation. For example, in countries where you ride on the right, a single mirror on the left side of your bar will cover almost all situations. Having a second one on the right is nice, as it covers your "blind spot", I consider it a luxury. 

In the end, everybody has different preferences with mirrors. You really need to try a few different kinds and brands and see what you prefer. There is a silver lining, though; many cyclists have unused mirrors. Chat up some cyclists if you have a club or friends who cycle, and someone will likely offer to lend you a mirror of give it to you outright.