As long as your car does not get destroyed or impounded before you log off, it will respawn in a garage 99.99% of the time. I have found bugs where it did not, but these are rare, and you can always replace the car for free with MMI if this happens.
As far as which garage it goes to, it depends on several conditions.
1. Did you buy the car from one of the websites, or did you steal it?
2A. If you stole it, which was the first garage you stored it in? If you have never stored it, it will be random the first time, then it will always spawn in the same one unless you move it to a different one.
2B. If you purchased it, then it gave you the option to choose which garage to have it shipped to. This is where it will always spawn unless you move it.
If you decide you would like your car to be stored in a different garage, you can always just transfer it by driving it from one to the other, as long as the new garage is not full.
If the new garage is full, then it will just send the car back to the old garage.
-Edit- If you stole the car, it will never respawn unless you have a tracker in it. You can get a tracker for free by driving the car into a garage, or buy one at any LSC. They will only respawn in a garage if you log off or pull a different car out of your garage, not if it gets destroyed, unless you buy insurance, which tends to be anywhere from 40 to 4000 dollars, depending on the value of the car. You automatically get both a tracker and insurance if you buy it from a website.
-edit 2- You mentioned that you could not find your car in the garages or on the map. This usually means that it was destroyed (players will destroy personal vehicles just for the fun of it), at which point you can get it back by calling MMI. There's also the chance that it was impounded, and you simply didn't see the symbol on the map. At this point, your best bet is just to pay the fee and get it back, or risk stealing it, but that is only useful if the car is in good condition and fast, and if you can get away without harming cops.