Check out this place!
Check this place out!
Are the two sentences above both correct? and if so, do they have the exact same meaning?
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Both are valid, and reasonably natural, if rather informal. The meanings are essentially the same. The first, with "place" at the end, may emphasize the place a bit more than the other. The second, ending with "out", is more strict;ly informal in usage.
a Google Ngram shows "check out this place" to be more than twice as frequent as "check this place out" in their collection of texts. However, in the "British" sub-collection, only the phrase "check this place out" occurs at all.