Alchemy mats used to be zone dependent but not for many years now so it's pretty much random what you find but obvious stuff like nirnroot/water hyacinth share spawn points near water, for example and the fungi are typically, but not always, found at the base of trees.

As for specific farming runs that depends on what you intend to do with them other than stock-pile. It's arguably more effective/efficient to farm imperial city for tel-var(tv) stones and buy satchels from the tv merchant for 500 tv stones each and/or farm gold and buy the alchemy mats. There's also the 'shadowy supplier' passive from the dark brotherhood skill line which can provide a 1/day bunch of alchemy mats

Ingredients for spell power potions (lady smock, cornflower, namiras rot and water hyacinth) are worth a bit as are any of the mats required for alchemy craft dailies at lowest/highest levels. But some of those, like mudcrab chitin, you'd have to do a tiny bit more than picking flowers.

But if you have eso+ I'd suggest you just enable auto loot and grab everything and from everywhere including looting any container; you can sort out the trash as needed and everything harvestable ends up in the craft bag including furnishing mats and fishing bait.

Also, while you have eso+ active, I'd also suggest choosing the hireling passsives for as many crafts as you can on as many characters as you can(maybe shadowy supplier, too, since your question is about alchemy mats); stuff like purple provisioning mats pretty much come almost exclusively from hirelings (other than daily craft rewards). With those passives, craft daily rewards and even just incidental farming your craft bag will start to fill quickly.