Usually _down the road_ and _around the corner_ mean something a little different, but it's possible they could be used interchangeably, depending on the layout of the roads. 

We can take a look at this little town and I'll explain. 

[![enter image description here][1]][1]

Let's say you are going from A to B. B is **down the road** from A (that is, they are on the same street), so I might tell you:

> You look hungry. Just go **down the road**, and you'll see a restaurant on your right. 

However, if you were going from C to D, C and D are not on the same street. So one way I might give you directions is: 

> There's a park **around the corner**. Head down this road and take your first left. You'll see the park on your right. 

The one place where the two expressions might be used interchangeably is when a road makes a sharp, near-90° turn, but it's still the same road. So, for example, if we were at E, and I was giving you directions to F, then I might say either one of these: 

> Just keep going **down the road**; you'll see the red building next to the bank. 

> Just keep driving until you go **around the corner**; you'll see the red building next to the bank.

Either of those would be accurate, although I might combine the two to make myself more clear: 

> Just keep going **down the road** until it makes a sharp left turn. Soon after you go **around the corner**, you should see the red building next to the bank. 


  [1]: https://i.sstatic.net/4k8Ldl.jpg