Any fast leveling techniques though? Maybe certain locations that are rich in ingredients which allows me to create lots of potions fast?
Create a huge stock of ingredients. Every time you complete an adventure, head to your favored home and dump them all in one area. For example, on the satchel on the Alchemy table in Breezehome. After you have a crapload, add them all to your inventory, put on any items that increase the strength of potions created, and create a CRAPTON of potions. Even if it's a worthless potion you won't use, it will increase your level.
Pick a place to store potions that you don't need right away or will sell later. I like to use the chest in the Breezehome Alchemy room on the bookshelf.
My favorite places to collect ingredients are the Reach (around Markarth), the plains around Whiterun (mainly to the West), and the swampy area south of Windhelm.
The Reach has Juniper berries EVERYWHERE, quite a number of mountain flowers, and lots of mudcrabs to collect chitin from (and petty souls).
The Whiterun plains have a lot of mountain flowers, lavender, mudcrabs, a small place with lots of bees, and lots of butterflies. At night, you can collect 2-3 times as many torchbugs and luna moths than butterflies. There is also a small patch of trees with around eight bees flying around.
The area south of Windhelm has Jazbay growing wild, plenty of mountain flowers (more than the Reach), lots of dragonflies, and creep clusters.
The marshy area Southeast of Solitude has lots of mudcrabs, the occasional nirnroot, and lots of swamp fungi. You may also find the occasional spiky grass pod, nordic barnacle, and guppy-like fish.
Along the coast of the sea to the north, you can find plenty of barnacles and spiky grass pods, as well as some nirnroot.
The Reach has lots of bears, so plenty of bear claws there. There also seems to be more deer here, so large and small antlers aplenty. Apparently, you can also find beehives around the Reach, but I normally only find them in certain areas. Beehives usually offer a bee, honeycomb, and beehive husk.
The other thing you could do is break into alchemy shops at night through the backdoor.
Mountain flowers can be found nearly anywhere. They are rather worthless, so they're great for making potions.
I think the Daedra Heart is too valuable for potions. They're priceless if your going to smith d
aedric weapons.
I agree for the fact that I've not created a potion that I can use or sell worth the same or more than the Deadra heart alone.
Thank you everyone for your extremely helpful advice, especially chelz0r!
So you think I should spend more time leveling restoration instead? I find myself using all my health potions very quickly. I use two handed weapons, which means I can only use healing spells when I'm not attacking which is quite difficult, meaning my only way of healing mid-battle is healing potions.
Well I guess I'll try and make lots of health potions with alchemy, for now.
Personally, I think you should work on Alchemy. It offers gold and useful potions for all activities. Restoration is much more limited. Switching from a slow, heavy weapon to a spell may also be plenty of time to get yourself killed. Clicking a potion happens at a pause menu, and the result is instant. A spell isn't.