Once you find the Leaky Cauldron, take your first left on to Diagon Alley. Around the corner is Knockturn Alley. They've got everything. But IF you have never been, I highly suggest you don't go alone.
What is it you are looking for in particular? We've got shops, cafes, schools, you name it.
I'm just down the road from Hogwarts school which incidentally was voted as the 36th best Scottish educational establishment in an online ranking, outranking Edinburgh's Loretto School.
If you're ever up in Scotland, give me a shout and I'll take you to the most exclusive tea shop ever - Madam Puddifoot's Tea Shop. It has the best pumpkin juice I have ever tasted. They also do chocolate frogs, cauldron cakes, Liquorice Wands, Jelly Slugs, blood flavoured lollipops and the best Cockroach Cluster this side of Godric's Hollow.
But to answer your question, we really do have "Wizards and Witches" Shops.