Both are correct:

Let’s check out that new restaurant!

Let’s check that new restaurant out!

However, if the direct object is a personal pronoun, we have to separate the verb:

Let’s check it out!

While native speakers are not consciously aware of this, the reason for the rule about personal pronouns is that the last word carries the most emphasis. Since a pronoun provides no new information, we don’t put it in such an emphatic position.

A: Should I turn the TV off?

B: No. Please turn the TV on.

Or “Please turn it on.”

A: Should I turn off the TV?

B: No. Please turn off the radio.