The most common and most likely answer to this crossword clue is the 4 plus 4 letter word SAME HERE
I've seen this crossword clue in Financial Times
S
A
M
E
H
E
R
E
More clues leading to the result SAME HERE
Buddy explains!

The straight part
We know that "Like this place/Me too" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case like this place/me too = same here.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.