for 'near' you may substitute 'around' Are there any restaurants around here? And yes, it is understood that you are only looking for one. But this is probably the most common way to say it here in America.

The difference between the two sentences is that the first is singular, while the second is plural. In the first you are asking if there is just one restaurant nearby. In the second you are asking if there are any. However, in general conversation, people will still understand that you are asking if there is any restaurants nearby when you use the phrase "Is there a restaurant near here?". Both are correct.

As Sofia told you, I think both are correct. For me the first one implies that you are asking for ONE restaurant (singular). In the second one, you are asking for ANY (plural) ... you could want to take a look at several restaurants before you choose where you want to eat.