Sorry if this is too new-ish of me but Applebee's sells alcohol so you need a CPL? Correct?
Rather you ask a question before the police come then after, don't be afraid to ask, ever! From the MOC tri-fold brochure, including legal cite and reference below. In plain english, you cannot open carry anywhere that is licensed to sell alcohol, even if they don't sell it currently. Applebee's does indeed serve alcohol, and is licensed to do so, therefore without a CPL you cannot carry there openly.
To clarify the other gentlemen's with a CPL question, you can not Conceal Carry at a bar (50% of income from poured drinks consumed on the premises.) Applebee's would not fit that description at all, as they are a restaurant and a bar. Anywhere that is a bar, the only way (I don't recommend it, but some do) you can legally carry in a bar or tavern is to oepnly carry your pistol and possess a valid CPL.
72cinjin and xj bmx, feel free to ask more if that does not clarify your questions and concerns.
What places are off limits to
firearms without a CPL? (Sec. 234d)
(1) Except as otherwise provided in
subsection (2), a person shall not possess a
firearm on the premises of any of the following:
a) A bank.
b) A church
c) A court
d) A theatre
e) A sports arena
f) A day care center
g) A hospital.
h) An establishment licensed under the Michigan
liquor control act.