Question: I've been invited to a business lunch in a non-Kosher restaurant. Can I attend and just have a drink?
Answer: The Mishna (Shekalim 3:2) writes that there is an issur derabanan to do certain acts which will give others the impression – maris ayin - that prohibited acts are permitted. R’ Moshe Feinstein (Igros Moshe OC 4:82) writes that there is a similar prohibition, chashad, which is giving others the impression that one is performing an averah. This would be prohibited mideoraisa.
R’ Moshe Feinstein (Igros Moshe OC 2:40) writes that one shouldn’t eat even obviously Kosher food in a non-Kosher restaurant, as others will either assume that the restaurant is Kosher (maris ayin), or assume that they are eating non-Kosher food (chashad). Only under extenuating circumstances would one be allowed to eat there. This would include either missing out on an important deal or being really hungry and having nowhere else to eat. Likewise, if one needed to use the facilities there and had nowhere else to go, they could enter. One should go in an inconspicuous manner and ensure that no one outside recognises them without knowing why they’re entering.
One is allowed to have a drink in a coffee shop that sells non-Kosher food, as others will assume that they are only consuming Kosher food (See Igros Moshe OC 1:96).