just my 2 cents but cheap bar and downtown seem to be at odds but then again, i actually don't like the library bar and find it about 15 to 20 years to old. just like most of the royal york honestly.
a few patios since rooftop places are not near the royal york....other than a small sliver at the trup but that place is not cheap and a little douchey last i was there.
patio here is good...
http://www.drakeonefifty.ca/ decent although a little hipster. pizza's are a decent option.
also, O&B patio is also nice....as is Jump's patio (same owners)
http://oliverbonacini.com/Yonge-Front.aspx
i was at this place the other day but i was pretty sloshed but food seemed decent. don't know how much sun the patio gets during the day but at night, it was fun.
http://www.socokitchenandbar.ca/
i think the closest rooftop place but so so food is
http://gretzkys.com/wayne-gretzkys-t...rooftop-patio/
and frankly, it feels a little like university.
ki and bymark are also near but i don't think either of them fit for budget but both have nice patio areas when you can drink on anothers dime....i would add the chase in this category also.