At most a piano player..uhm...Tom Jones steakhouse? I'm trying to remember a place that doesn't play any music. Really struggling...
Okay, here goes.
First time in Toronto, I'd skip the CN Tower (and One Eighty nee Panorama Lounge) and go to the Hyatt on Avenue road. Go up to the Rooftop bar (roof lounge or whatever they call it now). There's a south facing view and a walkout patio/balcony where you can take photographs of downtown core Toronto without a chain linked fence or a window with children and their grubby finger prints. It's a bar without a television - a proper bar. I think the Portuguese bartender who has been there since the 1960s still works there this year.
Similar establishments: Library Bar at the Royal York (no view, just history). I'm more partial to another Royal York bar (York Station - modeled after a train's bar car) but it's not open during the time you're over.
Thruth mentioned jazz. Don't know if you fancy it. If you do, a neat place to go is Jazz Bistro. It's a renovated jazz club in an old building. I don't usually go on the ground floor and pay cover. I go up to the top where they have an open patio in the back with some sofas (and unfortunately some televisions). Soundtrack is usually pretty quiet and you can have decent conversation.
Toronto Temperance Society - This is the place my liver hates. It's a speakeasy, windows all shuttered, dim lighting, pre-Prohibition cocktails, Billie Holiday in the background. You can skirt the members only swipe card door by going downstairs to Sidecar and either be very charming and say you want to check out this cocktail bar and see what membership would be like...or buy a drink and ask about the place - they usually boost you upstairs. (or find me) No televisions, no mobiles.
Similar establishments: Civil liberties, Museum Tavern (all sorts of whisky flights), DW Alexander..but they are a lot louder. Same décor.
Midfield Wine Bar - I usually take wine lovers here. They do flights and mini tastings. More like a neighbourhood type place. They serve food but I've always skipped it.
Queen & Beaver - this is really the only proper pub in the city. Don't get a table downstairs with the host/hostess - just walk upstairs. Quietest times would be 11am when they start alcohol service or mid afternoon (3pm). I don't remember them playing too much music. They have the usual library, papers, couches, and a small balcony. Only one television that only turns on for footy, rugby or cricket. When I'm not engaged on weekends, I kill a few hours here with a pint of Pride.
French places - I have a personal favourite but it's love/hate: Le Select. I love coming here with the ladies and popping open a bottle of wine and cheese plate.
Alternatives: La Societe (copy of Balthazar), Cluny (bonus, you get to see the Distillery District), Alo (this is new, I haven't been but I heard nice things, 3 floors up from a burger place at a busy intersection - tasting menu only).
One bar I went to recently was Bar Raval. It's a tapas/pintxos type place. Mostly standing room. Interesting décor. But quite loud at pretty much all times of the day except mid afternoon or early in the morning (but then you don't get booze). There was a queue at 12am on a Tuesday the last time I was there.
Another that I come back quite often just for the view is The Chase. Go down the alley, go inside. Don't go to the fish & oyster ground level restaurant. Take the lift up. There's a bar that is half inside and half outside. If you sit outside, I think it's quieter when the patio isn't full. If you sit inside at the bar, you can see the 360 degree wrap around window restaurant. I don't remember the music being too loud. It can get very busy though. More of a place for posh people to blow money on $75 chickens.
Alternatives: Beverly Hotel Rooftop Bar, but the music is loud. Sweet talk the bartender/hostess on the main floor to use the lift or you have to hike it up the stairs because you're not a hotel guest.
I can think of many more places but your volume requirements are a bit restrictive.