EDIT: FOUND AN EVEN EASIER PLACE!!
I got a X10 after only 10 seconds or less in the area. It has a mutant nest (aka "Mutie Nest" in the game) and the mutants just keep running at you. No armor guys from what I remember. I just used the assault rifle. I wast even trying and I looked down to see my multiplier maxed out. I'm sure any mutie nest will work but the one I used is in the Torn Plains region, right in the middle bottom just as you cross into the region from the Broken Tract region. I got a X10 here MANY times without even trying. I am pretty sure the enemies are infinite as long as the mutant pods have not been destroyed.
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Edit 2: If you have the smart rocket (In the strongbox ark located in the right center of the Torn Plains region); when using it with overdrive, it's pretty crazy and can eliminate a ton of enemies at once.
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I found a very easy place to get this close to the beginning of the game. I found this place immediately after completing the "Blackout" story mission, which is the mission you get the shotgun in. Could get this 2 or 3 times in this area in one go. I bet there is 30 enemies here. The annoying thing about this area is that there is a lot of armor enemies but if you hit them with the slug rounds my holding the left trigger with the shotgun they are not too bad. They can be bullet sponges so make sure you kill them and not just send them flying 40 feet back.
You can make a save at the beginning of the area just in case. If you feel like you are going to fail, just let them kill you and it will start you right at the beginning of the base. Took me maybe 3 or 4 tries.
The area is called Yeoman Growery and it's a Bandit Den in the Northern part of Broken Tract. I HIGHLY recommend having the shot gun as it was the main gun that I used. Make sure you buy the project that unlocks the ability to get to a X10 multiplier. It's located in the basic project upgrades and cost 1 point to unlock. I ran into this area throwing grenades everywhere. Took out the guys up front and then ran through the middle letting them all run at me from all directions and then activating the overdrive. I believe overdrive makes this a lot easier. So if you want try and go through the project upgrades and buy the stuff that helps overdrive and maybe the ones that allow you to carry more throwables and ammo.