A verb meaning "to look around making sure no one sees you"

It sounds as if they're making furtive glances. From the linked definition:

attempting to avoid notice or attention, typically because of guilt or a belief that discovery would lead to trouble; secretive; suggestive of guilty nervousness.

To address a comment by @talrnu that a furtive glance is a discreet action in the company of others rather than a check for the presence of observers:

I recognize your meaning but find it restrictive.

In any case here's another possibility - on the qui vive defined as being on alert and watchful, as a sentry on post.

Looking over one's shoulder [Oxford]

Be anxious or insecure about a possible danger:

It's usually figurative, but it could work here.

To be on the lookout or on the alert (for someone or something) may fit your context:

• watchful for someone or something. Be on the lookout for signs of a storm, be on the alert for possible intruders.

The Free Dictionary