A "posh restaurant" refers to a high-class or fancy establishment where people go to eat fine, expensive food in a luxurious environment. Full definition
I love eating at posh restaurants and trying new cuisines that I don't have in my repertoire,... (fitbodyhq.com)
Alinea chef Grant Achatz ignited debate over a baby ban in posh restaurants after a crying tot spoiled other guests» dinner. (articles.chicagotribune.com)
When preparing for a date, you'll be thinking of what to wear (you're looking online for a new pair of jeans) and where to go (that posh restaurant with a pricey menu). (uk.match.com)