What is the best way to get tons of soul gems to grind enchanting to 100? Just fast travel between towns and buy from the court wizards?

Dwemmer machines like the spiders almost always have gems. In black reach there's geode mines which can produce soul gems and random ore.

This- go clear some dwarven ruins, the machines have them for "power" supplies. Creepy if you think about it, since many of the gems are filled.

Places like Forelhost.... I think I wound up with 20 petty gems the last time through there, some of them filled. And a few larger ones, empty.

Dwemer ruins, any spots where necromancers hang out, even Draugr crypts seem to be good sources of them. There's a fair number of them laying around the College of Winterhold, but some of those will have to be stolen.

There are also lots of soul gems, filled and empty, in the invisible Dawnstar chest.

Dwememr ruins, the number one place for soul gems. I ended having to store groups of filled gems in cabinets in my homes because I was getting weighed down. I had like, 50 filled greater, 60, filled common and easily over 100 filled petty and lesser.

Blackreach has got many Geode Veins, which give you soul gems rather than ores.

You can increase the Enchanting skill by just recharging your weapons. With the Star of Azur and Soul Trap on a weapon can you recharge your weapons many times and thereby increase your skill while you continue to explore caves and ruins. Start using enchanted weapons early in the game and keep them charged and you do not have to stand at an enchanter to grind it up.

Mage's College. Once you are the arch mage, the staff just spend their days standing around the main hall. They ALL sell soul gems (at least if you have Merchant perk, not sure otherwise) so you can pick up 40+ in one quick round of shopping. Enchant Banish daggers and Sneak boots, sell them for money for more soul gems, etc.
This assumes you are good with filling those gems, of course. I built an enchanted daedric greatsword for that job...