Tough one.
From an historical perspective, The Mansion House is the oldest licensed tavern in Canada.
They do have a lot of live music there. From a culinary perspective, it's a bar with a boring menu.
My first thought though was The Port Mansion, overlooking Lakeside Park (yes that one) in Port Dalhousie. However, it's been torn down to make way for stalled development projects.
So, I'd probably go with The Valley Restaurant in the north end of the city. It's been in operation since 1953. It's in the middle of a residential area and very much unknown, but good food and nice atmosphere.
And now, the Valley Restaurant is up for sale.
From the perspective of the region, there are a lot of restaurants that do the farm to table style of cuisine very well.
If you want fancy, go to Windows by Jamie Kennedy in Niagara Falls. I'm biased because he's my sister's ex-husband, but we still claim him as our brother-in-law.
However, he's also pretty much responsible for the whole farm to table concept in Ontario (if not on a broader scope).
As far as a culinary experience is concerned, but without a huge price, I'd probably suggest an all day tour of the wineries, craft breweries, and distilleries.
There are tour companies that do it, but it's better to have a local organize something (and a designated driver).
One of the distilleries does a brunch on Sundays in the summertime.
Two of the breweries do lunch and sometimes dinner events.
Most of the time these are done by guest chefs from local food trucks - but gourmet chefs - and they tend to stretch out the menu a bit from the food truck fare because they have a commercial kitchen to work in.
Then, almost all of the wineries have restaurants. They can range from an outdoor bar with a wood-burning pizza oven to wear-a-jacket-you-filthy-heathen fine dining and everything in between.