As the person being quoted–I use the term “nice restaurant” to mean “upscale.” Not “good”, there’s plenty of great places I can tell you in the Northern Virginia / Richmond corridor that are great food and will be under $15 a person if you want it to be. Most people I know when they say nice restaurant do mean upscale. Examples in a sentence, “I’m taking Mom out to a nice restaurant for Mother’s day.” This implies it’s somewhere more upscale, where you’re willing to spend a little more.
It doesn’t have to mean fine dining, lots of trendy and nice upscale restaurants do not adhere to “formal fine dining” (i.e. the waitstaff aren’t wearing black tie, there isn’t a formal course-structure to all the meals etc"), but some characteristics of “nice” restaurants usually: a wine list, with at least a few really good wines, the head chef is known–either on the restaurant’s website or menu or signage (because it’s a real head chef, not a head cook running a shift at Applebee’s), decor and cleanliness are important–it doesn’t have to be a formal setting, but it shouldn’t look like a Denny’s, they should take reservations, there should be someone offering to check your coat for you at the door, if it’s in an urban center there should be valet parking. Some things that you’ll see most of the time at a “nice” restaurant, but not necessarily always: prixe fixe menus, tasting menus, very focused menu around a specific kind of cuisine, use of only fresh ingredients, professional pastry chef on site in addition to the regular head chef.