Small Singapore: How Could a Website Be Benificial?

Now the Question that Business owners of Singapore (Especially retails / service)

A small business that's only targeting the locals, or a certain district to be more exact. Would a website benefit them?

Let's say you have a shop in Bedok, that's the eastern side of Singapore, and you're only targeting towards customers who are at Bedok. How could a website benefit you?

Now, Singapore is small. You might have to agree with me on that.
A good example would be, have you ever traveled towards the other end. (Let's say you're staying at the West End, and you traveled to the East End just to enjoy a good bowl of noodles or something that has caught your attention through word of mouth from your friends)

Singapore is small to the point that, you shouldn't actually think your clients would only be in your district area.
It's much more appropriate and beneficial for your business if you think that the whole island as your potential customer.