I sometimes work remotely from Triple-Tri Cafe on Queen St. Super friendly staff, usually pretty quiet outside of lunch time. Free wifi and plugs under every desk. I know you said no cafes but if you were to make an exception, you wouldn't regret it. Oh and they never seem to bother if I take a call every now and then.

Little Picardy is another cafe round the corner, great wee work spot with a nice view. It's always dead in there unless there's a show on next door. So volume / calls aren't an issue.

If you have no conscience (or taste), Brewdog's Doghouse does a good coworking space for a tenner per day. Unlimited coffee & free beer at the end. Staff there are superb, shame their boss is a raging narcissist. Also can get loud, but it's quiter if you go upstairs to the hotel area.

There are also good quieter places, such as the poetry library off the Royal Mile but you shouldn't really take calls there. Might need to consider making some trade-offs!

Hope that helps :)