Dropped monitor - cracked 1/4in jack :(

Well, I normally would suggest Radio Shack but they are adio S. You can order it from Allied Electronics.
 
https://www.alliedelec.com/switchcraft-12a/70214523/
 
Another option for you is some place local like
Electronic Connection
37387 Ford Rd
Westland, MI 48185
(734) 595-6655
 
There are 2 types of 1/4" jacks. One is 2 wire (mono) and a 3 wire (stereo). Either will work. Just use the inner most terminal and outer shell connections if you get the 3 wire. Solder it in and you are golden.
 
PS: You might check the thread length of the one you have. If the jack is mounted in some think material you may need the 1/4" threaded one instead of the 5/32" (0.156) long thread.

If you have a local radio shack give them a try. If not, it's a 1/4" mono female audio jack online. They aren't expensive. A small adjustable wrench and a soldering iron should be all you need. You can use a cheap pencil soldering iron. I think Newegg has them. Any radio Shack also does. 60/40 rosin core solder. Melt some on the tip of the hot iron to tin it. Rub it off with a wet rag or a sponge. The tip will now look shiny. Careful!!! The iron is HOT!!!!  Install the new connector and solder the cut and stripped wires in place. It helps to also tin the wire ends before you join it to the connector.  The process needs to happen fairly fast or the cheap iron will overheat the wire and burn the flux away. One the iron is up to temp all it takes is a brief touch on the connector, then feed the solder onto the heated junction point. If the tip gets black or the wire insulation begins to melt, it was overheated or the tinning burned off the tip.
 
So the tip touches it, stays on a few seconds, once hot enough to melt the solder feed the solder using your other hand, just a little of it. Iron comes off immediately. Done!

When you say the wires go directly to the speakers? That seems odd, there should be a crossover. 
Anyhow in a pinch if you don't have an extra jack around you could hardwire the cable. Make sure the tip is + 
That will get you back in business. 

If you can't find a way to fix it yourself, here's a used pair for $50:
 
http://www.guitarcenter.com/Used/Alesis/Elevate-3-Pair-Powered-Monitor-113553446.gc
 
There's also another (cleaner-looking) pair on Ebay at around the same price.

I thought of a HIGHLY POSSIBLE other solution - these bookshelf monitors connect using a standard 1/8in M-to-1/8in M cable. What if I removed the jack from the box and connected the wires of the 1/8in cable directly to the internal wires of the box? Which wire connects to which (etc) matters, obviously, but it's just two wires connecting two wires. And then I could run the cable straight out of the hole that the jack was mounted in and it'd be like new.
 
Of course there's something to be said about actual monitor stands to avoid this issue in the future.
 
I may just do it today as its a seemingly very easy procedure, but first I wanna know if its possible! I'm also tired of having the one side of my system sound like a cardboard box because the back isn't mounted on.
 
Pic below:
" />
 
 

Cactus Music
Unless that's a shadow, am I seeing 3 wires? I see one red and 2 black? 
Naw, it looks like a shadow. 
Anyhow my guess is the RED is positive which is the TIP of your patch cable or the none braided wire when you open a patch cables jack to take it apart. 
 
So an option is to sacrifice a patch cable, wack the end off or just un soldier it from the jack and soldier that to the wires inside the speaker after you cut them free from the broken jack. 
 

Nope - used flash so it may give the appearance of a third wire. But thanks, Cactus! This is the exact solution I was looking for - juts couldn't put it into as good technical words as you did there. Thankfully, if this for some reason DOESN'T work out, I'm only out of a cheap cable realistically. I'll post my results later on tonight!