The Cronvangr Cave in Eastmarch is full of weak spiders, I usually hunt there.
Map, courtesy of the Elder Scrolls Wikia :
gaming.stackexchange.com/users/14981/Yannick
Look up info on the questline to get the Black Star, which is a reusable soul gem that will take a humanoid soul (which seem to always be grand).
Then any old bandit can be sucked up into that thing.
Also, draugrs and skeletons and the like are White souls, so you can just go in a dungeon with a bunch of those guys (with a weapon enchanted with soul trap) and suck them all up into gems.
gaming.stackexchange.com/users/14945/Andy
The easiest way I've found to get petty souls is simply to kill random creatures like foxes, deer and goats.
Nearly anything that moves can yield a soul, and you'll find these creatures in tremendous supply throughout the world just in the regular process of moving from place to place.
gaming.stackexchange.com/users/13304/Cypren
The best way I found to fill up petty soul gems (and fast) is starting from whiterun and following the river down killing all the mud crabs I find.
They are easy to kill and will attack you if you approach them so it a good excuse to disintegrate them (as i dont like killing creatures for no reason) xD.
gaming.stackexchange.com/users/15324/Ciskje
I've had a great deal of success with the wanton slaughter of chickens and other livestock.
Be advised however, some companions won't stand for it.
I tried it with Lydia following me, and she left my service, and tried to kill me.
And of course, if there are any other witnesses, you could end up with a bounty and some angry townsfolk.
gaming.stackexchange.com/users/3129/LessPop_MoreFizz
Isn't it enough for you to pick them up from bandit lairs or from shops of people who like you?
I also do a lot of enchanting
and I always have a lot of spare souls in my pocket, mainly owing to collecting them from various locations.
gaming.stackexchange.com/users/5809/Hiena
The path to High Hrothgar is also full of small animals that you can use to fill your gems.
gaming.stackexchange.com/users/5925/Chris
I think Blackreach is a nice place to go, because the dwarven machines all give white souls and a soul gem, usually filled.
You can also mine more soul gems from the ore veins.
gaming.stackexchange.com/users/22104/user22104
When I need to fill up a surplus of petty-to-common soul gems for leveling up enchanting, I fast travel to a location far West of Whiterun then travel straight East until I am far East of Whiterun.
Spanning this distance allows me to kill scads of mud crabs, wolves, deer, and foxes at an easy distance with my Bow of Soul Suck.
I'll fill up 20 or 30 soul gems in no time.
Unrelated to your question, I'll then enchant a bunch of iron daggers with Daedra banishing, fast travel to various item vendors, purchase all their soul gems (even greater and grand), and then break their bank by selling them my expensive daggers.
Now I get more soul gems and level up my speech in the process with all the bartering.
With all the pelts I collect, I smith up more iron daggers or leather bracers (if I have no iron ingots) to top off my smithing.
Then I'll enchant the daggers with Daedra banishing and reinse and repeat until it's time to go hunting again.
gaming.stackexchange.com/users/10570/oscilatingcretin
Go Dragon Bridge and then start to follow the roads.
Always sneak because there are tons of mud crabs, elk, deer, bunnies and other petty-common souls waiting for you to capture.
Sources: Level 100
every skill no life
gaming.stackexchange.com/users/30187/TACxVengeance
Go to a Nordic ruin and start slaughtering normal draugr with soul trap weapon.
gaming.stackexchange.com/users/42953/Hipnog
Mudcrabs .
Unlike the spiders, they respawn fast, within days.
Unlike other general wildlife, they are hostile, so you don't have to chase them down.
Unlike bears, horkers, and draugr, they are easy and can be killed at a low levels and one-shotted at high levels.
I cycle through the following locations:
Spiders at Cronvangr Cave Mudcrabs at Mara's Eye Pond Mudcabs in water running southwest from Halted Steam Camp If I still don't have a enough souls after that, I literally find a nearby river and just start running down the banks of it looking for mudcrabs and killing any wolves or other wildlife nearby.
gaming.stackexchange.com/users/6770/Chris Redford
Go far east of Winterhold, where all the icebergs are and you will find like 10 bears, 20 wolves, and near 15 horkers.
I went there and I found a ton of soul gems I probably filled my accounts savings of soul gems in that one run.
gaming.stackexchange.com/users/41268/Dah Battlemage
Get a bow and enchant it with soul trap.
Pick up some arrows for it too.
(They weigh nothing, anyway, so you might as well pick up all that you find.)
Go hunting in the woods.
Almost any random wildlife will yield a petty soul; even rabbits will do.
Most of the smaller critters should die with one shot.
(If not, find a better bow.)
As a bonus, you'll pick up pelts to train your smithing with, as well as the occasional alchemy ingredient and other random loot.
If you don't like bows, the chase-and-stab technique will also work for most animals, although deer tend to be too fast and skittish to be easily caught that way.
A few larger animals even have bigger souls:
sabre cats have lesser, bears have common and mammoths actually have grand souls.
Not that you'd want to hunt any of those things with a bow, unless you're actually good with one.
gaming.stackexchange.com/users/13833/Ilmari Karonen
I'm training my enchanting skills and the limiting factor currently is the availability of filled soul gems. Most vendors only have very few of them or none available, and they are also considerably more expensive than the empty ones.  I'd now like to fill up my collection of petty soul gems with souls. Are there any areas with respawning low-level creatures that I could use, or is my only chance to randomly roam Skyrim and hope that I find suitable creatures?
Where can I find lots of petty creatures to charge my soul gems?
gaming.stackexchange.com
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gaming.stackexchange.com/questions/36623
gaming.stackexchange.com/users/4103/Mad Scientist
The easiest way is to kill random creatures like foxes, deer, goats and weak spiders. You can also try slaughtering chickens and other livestock.  It is apparent that killing small animals and creatures can provide petty souls.
It is apparent that killing small animals and creatures can provide petty souls.