Stores in diagon alley:

2nd hand brooms- sells used brooms 

Amanuensis Quills-A shop in Diagon Alley that sold quills. It was next to Madam Malkin's Robes for All Occasions.

Apothecary- A store located at North Side, Diagon Alley which supplied merchants with ingredients for potion-making.

Broomstix-A shop that sold broomsticks.

Eeylops Owl Emporium- A pet shop located in Diagon Alley that sold owls and various other things needed for the care of owls, like Owl Treats. It sold a variety of breeds, including screech, barn, tawny, brown, and snowy

Florean Fortescue's Ice Cream Parlour- It was a shop selling ice cream and was owned and operated by Florean Fortescue, and was located at Diagon Alley

Flourish and Blotts-A popular bookshop in Diagon Alley where most Hogwarts students purchased their schoolbooks

Gambol and Japes Wizarding Joke Shop- Gambol and Japes Wizarding Joke Shop was located in Diagon Alley. Fred and George, and Lee Jordan stocked up on Dr Filibuster's Fabulous Wet-Start, No-Heat Fireworks 

Gringotts Wizarding Bank-Gringotts was the only known bank of the wizarding world. It was created by the goblin Gringott. It was located in Diagon Alley and owned and run by goblins. In addition to storing money and valuables for wizards, one could go there to exchange Muggle money for wizarding money

Healer Shop-The Healer of this shop altruistically offered free treatment at her healing station, seeing it as her duty

The Junk Shop- A shop that sold secondhand items such as broken wands, lopsided scales, etc

Leaky Cauldron- A popular wizarding pub in London. It was the entrance to Diagon Alley

Madam Malkin's Robes for All Occasions-Sometimes simply referred to as Madam Malkin's, it was a shop in Diagon Alley where students got their Hogwarts school uniforms, and also dress robes, travelling cloaks, and the like

Madam Primpernelle's Beautifying Potions-Located at 275 Diagon Alley, this shop helped witches getting rid of "warts and worse.

Magical Menagerie-One of the shops where students bought their pets and supplies

Obscurus Books- Located at 18a Diagon Alley, Obscurus was a wizarding book publisher. Its range of titles included the popular Fantastic Beasts and Where to Find Them.

Ollivanders-Ollivanders was the sole wand shop of Diagon Alley. Peeling gold letters over the door of the shop read: "Ollivanders: Makers of Fine Wands since 382 B.C.". The shop's display consisted of a solitary wand laying on a faded purple cushion in the dusty window. The shop was tiny, empty except for a single, spindly chair in the corner. Thousands of narrow boxes containing wands were piled right up to the ceiling of the tiny shop, and the whole place had a thin layer of dust about it

Potage's Cauldron Shop-A shop that sold cauldrons.

Quality Quidditch Supplies- A shop in Diagon Alley. Its main products were things having to do with Quidditch such as Quaffles, Bludgers and broomsticks.

Rosa Lee Teabag- A teashop located in Diagon Alley as well as in Hogsmeade.

Scribbulus Writing Instruments- A shop that sold ink and presumably other stationary items (quills, parchment)

Second-Hand Bookshop- A shop that sold second-hand books 

Second-Hand Robes- A shop that sold second-hand robes

Slug & Jiggers Apothecary- This was where students bought their potion ingredients

Sugarplum's Sweets Shop-A shop that sold confections

TerrorTours-Located at 59 Diagon Alley, TerrorTours was presumably a travel agency for wizards and witches.

The Ministry Press- A publishing house affiliated to the British Ministry of Magic

The Daily Prophet's main office-Presumably where the Daily Prophet newspapers were printed.

Twilfitt and Tattings- Twilfitt and Tattings was a wizarding clothing shop located in Diagon Alley. Given that it was favoured by elitist pure-blood witch Narcissa Malfoy, it was probably an upmarket shop.

Whizz Hard Books- Located at 129B Diagon Alley. Whizz Hard Books was a wizarding book publisher. Its range of titles included the popular Quidditch Through the Ages and Hairy Snout, Human Heart

Wiseacre's Wizarding Equipment- A miscellaneous equipment shop

Stores in knockturn alley:

Borgin and Burkes - An antique shop.

Beard Trimming - A barber shop.

Betting shop - A shop that takes bets on various events. 

Chimney Sweep Elf

Cobb & Webb's - A shop that sells items related to Dark Arts.

The Coffin House - A shop that sells Dark Arts materials related to the dark art of Necromancy.

Dystyl Phaelanges - A shop that sells bones.

E.L.M and Wizards Undertakers & Embalmers

Fledermaus and Tanner Bats & Skins

Markus Scarrs Indelible Tattoos

McHavelock's Wizarding Headgear

Moribund's

Mr Mulpepper's Apothecary - A shop that sells potion ingredients.

Msaw Ætare

Noggin and Bonce - A shop that sells shrunken heads.

Potage's Cauldron Shop - A shop that sells different types of cauldrons.

Tallow and Hemp Toxic Tapers

Trackleshanks Locksmith

Shyverwretch's Venoms and Poisons

The Spiny Serpent

The Starry Prophesier

The White Wyvern - A pub.

Wizarding Supplies

Ye Olde Curiosity Shop - A shop where people can purchase curios related to Dark Arts.

shops in hogsmeade: 

Honeydukes–  a sweet shop that had the entrance to a secret passageway into Hogwarts in its cellar.

Hogsmeade Post Office

Tomes and Scrolls–A specialist bookshop that was established in 1768.

Hogsmeade station– the railway station

Wizarding Wireless Network Headquarters –Main headquarters of the popular radio station.

Spintwitches Sporting Needs– A shop that sold sporting goods.

The Magic Neep –A greengrocer's. 

1753. Pippin's Potions – A chain of apothecaries established in 1753.

Zonko's Joke Shop– A famous joke shop

Dervish and Banges– A helpful shop that sold and repaired some magical instruments.

Scrivenshaft's Quill Shop– A shop for all types of quills.

Three Broomsticks Inn– A pub owned by Madam Rosmerta.

Ollivanders– a branch for ollivanders from diagon

Hogshead  Inn –A dingy pub owned by Dumbledore's brother, Aberforth Dumbledore, which hosted a secret passage into Hogwarts created by the Room of Requirement.

Madam puddifootsTea Shop –"The haunt of happy couples", according to Harry Potter. Usually couples went there on dates.

Ceridwen's Cauldrons-A shop that specialised in cauldrons. 

Dogweed and Deathcap–A Herbology shop.

Dominic Maestro's Music Shop – A music shop ran and operated by Dominic Maestro.

Gladrags Wizardwear –A clothing shop that also sold very lurid socks, including ones that screamed when they got too smelly.

Hairdressing salon –A hairdressing salon where students got their haircut done. It was across the street from Honeydukes.

Hayden family shop A shop owned by Corey Hayden's parents.

Hogsmeade branch of Potage's Cauldron Shop –A Hogsmeade branch shop that sold cauldrons.

Offshoots in knockturn and what you can find there:

Impar alley - for the odd and different.  

Jiggery Deli-There are no waiters, or menus, or fellow patrons. When you give the password the doorway takes you to a set location, which to my knowledge is different every time you visit, and a table appears for the exact number in your party. We will sit, I will place the required amount of coins on the table, and a predetermined meal will appear before us.”

Contrair alley- for all the dark things.

Sanguis alley- where the vampires hang out

amissa anima alley-for the lost souls looking for a place to stay.