I'm surprised nobody else has said it yet
but, BLACKREACH!
The area of the dwarven ruins Alfrand with the crazy giant glowing mushrooms.
The main quest line brings you here to get the elder scroll.
There are a million dwarven machines that drop them, the falmer carry them sometimes, and finally, and the best part, you can mine them .
Bring your pickaxe.
Look for "Geode Veins.
"
I haven't seen it mentioned anywhere else
but a geode vein is where soul gems come from.
You mine it like just like iron or ebony ore.
I suggest using a weapon enchanted with soul trap also because every falmer you kill will go right into filling an empty gem.
When I got done I had about 60 or so filled soul gems and leveled from enchanting 50 to 100 with the one trip!
Do the quest to find 30 crimson ninroots while you're at it
and you'll run into all the geode veins.
gaming.stackexchange.com/users/17038/TMC
When I wanted gems for enchanting
I just went back and forth between Calcelmo in Understone Keep(Markarth) and the Wizard in Dragonsreach.
gaming.stackexchange.com/users/14445/JingleDix
It's a roundabout way to solve this: Complete The Black Star quest for Azura.
You can either get a reusable black soul gem or a reusable grand soul gem (which you can then fill with petty souls to your heart's content).
gaming.stackexchange.com/users/7111/The Communist Duck
Complete the black star quest (research it).
Make sure you have no soul gems in your inventory.
Learn soul trap enchant (buy a weapon from a merchant and disenchant it).
Enchant soul trap on your weapon, then kill something to refill the black star quest reward.
Recharge your weapon, rinse and repeat.
Using this method I reached 100 Enchanting in an hour.
gaming.stackexchange.com/users/14917/Shaun
If you hop between Calcelmo in Understone Keep (Markarth) and Wylandriah in Mistveil Keep (Riften)
they will always have restocked since round-trip is about 54 hours (42 to restock).
Wyldanriah is also a short distance from entrance.
(I should mention Understone<->Mistveil is also very useful when seeking the Banish enchantment as the blacksmiths are near as well.
Oh and remember if you're married these time elapses can be profitable.)
If you're fast on your feet (high stamina, no armor or penalty, Whirlwind Sprint) the jaunt from Mage to General Store in both towns may be worth it.
For my test character (starting stamina, no armor, no shouts) from conversation-tree to conversation-tree: Mage->Mage, 1 minute Mage->General Store, Riften, 30 seconds Mage->General Store, Markarth, 45 seconds (for both running & fast travel to entrance)
I used set timescale to 150000 for instant vendor re-stocks, and the mages do carry on average more empty Petty Soul Gems than the general store, just enough that I think my Level 1 is too slow for the complex routes.
gaming.stackexchange.com/users/2484/Christopher Galpin
I just figured this out and I wish I had sooner:
There are about 30 filled soul gems available for the taking in the College of Winterhold
(check both the Arch-Mage's Quarters and all the dorm rooms).
Once you take them all, simply wait two weeks (takes about ten minutes real time) and then all of the gems will have respawned.
For me, this has been the easiest way to get soul gems yet.
gaming.stackexchange.com/users/17439/Pat
Go to Dawnstar, wait until the khajiit caravan is in town, and then go to the chest take all the soul gems.
Go back to the khakiit camp, talk to the trader, wait 49 hours while looking at the trader (They wont leave town if you're watching them).
I find it helps a lot to wait the extra hour, then go back to the chest, take gems.
Rinse, repeat, be happy.
gaming.stackexchange.com/users/31488/Kross887
The Riverwood Trader in Riverwood has a lot of soul gems for me usually.
If not, I go to Calcelmo in Understone Keep.
gaming.stackexchange.com/users/15347/James
I go to dragonreach buy all his gems.
Savegame, kill wizard, reload.
Buy more gems etc., rinse and repeat.
Works with all NPCs as well and is way quicker than waiting 48 hours for them to replenish stock and gold
gaming.stackexchange.com/users/17177/Maelstrom
In the dawnguard dlc the soul Carn just about every skeleton has soul gems on them filled like black or grand
such and such I got
so many last time I went and it was so easy.
So much better than wasting your money on buying them.
And if you wanted to soul trap just for conjuration exp then just spam cast soul trap on a dead body.
Goes by fast if you make 4 items with 25% less cost magica on each of them
so your conj spells cost no magic and just span soul trap.
It gets to 100 so fast
gaming.stackexchange.com/users/30814/Jabezz
What I do is buy from the jarls wizard in Dragonreach then save the game, kill him, load save, buy more, save and kill him again, then load again and keep repeating the process.
He restocks every time you reload. :)
gaming.stackexchange.com/users/17128/Danny
Tolfodir sells them in the College of Winterhold.
Wait 48 hours and he replenishes (requires 2 wait periods).
But you can sit there in one place which is nice.
Just about to hit 100 enchanting and put double enchantments on all my gear :-)
gaming.stackexchange.com/users/23470/JRome
Soul Cairn from the Dawnguard DLC is a great place to farm soul gems - every enemy will drop either an empty or filled soul gem of random size, including black soul gems.
You will unlock this area as you play through the plot of the DLC.
gaming.stackexchange.com/users/19827/kotekzot
I would like to buy lots and lots of Soul Gems. Petties etc. It's to train Enchanting.   I can't find a reliable source that constantly has a good supply.   (Aside from Collette at the Mages College, and the Wizard in Dragons Reach, I can't find anyone else?)
Where can you acquire massive amounts of Soul Gems?
gaming.stackexchange.com
<the-elder-scrolls-5-skyrim>
gaming.stackexchange.com/questions/36374
gaming.stackexchange.com/users/12173/Layke
You can mine for them or you can hop between Calcelmo and Wylandriah as it will have restocked in between. You can also go to dragonreach and buy all his gems. This goal could be achieved through a variety of described processes or quest completion.
Soul gems could be acquired by completing quests or exploring certain locations. There are several ways to acquire Soul Gems involving waiting, fast travelling and saving/loading game.