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.