I am not one for large loud club scenes, but a small quiet bar fits me best. It appears the only ClubCorp place in Vegas has shut down so I would appreciate any help from the locals.

I know that the Palazzo has a special hospitality floor with a bar limited to hotel guests on that floor.  I believe there are similar exclusive areas in the Venetian and Wynn properties.

The Petrossian Bar at Bellagio. Go to the back and sit either at the bar or one of the small tables near the bar away from the entrance.

I'm the same way, I love quiet places to truly relax and imbibe.
So!
The Trump lobby bar is a big fav- I even have a Come to Jesus meeting couch I favor-elegance, true luxury and cocktails are very reasonable
The Franklin at the brand new Delano- stunning!
As is the Foundation Room before the party scene hits, so 5-10pm
The Peppermill lounge is a perineal fav: sitting down along the fire/ water pit mesmerizes me.  
Humm...
Oscars at the Plaza Downtown
Downtown Coctktail Room before 10pm-
Bali Hi golf course-

It is in the walkway between Paris and Bally's, it is a piano bar/lounge with an old Vegas feel.

Not very quiet in there!

It's deafening just walking by the place!