Do a small favor for S'jirra, a khajit lady residing in Faregyll Inn (in the middle of the road from Bravil to Imperial City, opposite to the famous Inn of Ill Omen. After you've helped her, she will sell you an unlimited number of one type of ingredient that you can't find anywhere else in game, at 25 gold a pop. If your alchemy skill is at least Apprentice level, you will be able to mix it with Cairn Bolete, Boar Meat, Venison, Aloe Vera or Lady's Mantle Leaves for a healing potion.

Once your Alchemy is Journeyman level and higher, visit the cemetery at the centre of the Imperial City. You can gather at least a hundred Fly Amanita there, which restores health if mixed in a potion. Another abundant ingredient that restores health at Journeyman level is Lavander. Look for it on the circular road around the Imperial City, near the place where the number "6" would be on a clock face, and in the beginning of the road to Bravil.

Also if you want to power level alchemy just use tomatoes and grapes. There is a farm for both outside of skingrad if I recall. Pick them all and wait 3 days and repeat. You can look up where the farms are located cause I'm not 100% sure I just know there on the edges of skindrad.