Westeros is approximately the length of South America. GRRM says 'size' as a shorthand, but it's not accurate. From the Wall to the south coast of Dorne, Westeros is almost exactly 3,000 miles long. Based on the length of South America, that leaves at least an additional 1,400 miles or so north of the Wall. Westeros is never more than 900 miles wide at its widest point (or about one-third the width of the United States) and frequently much thinner than that.
The easiest way to figure things out is to use the Wall as a scale bar. It's almost exactly 300 miles (100 leagues) long. GRRM originally said you couldn't use it as a scale bar because he wanted to protect himself from being pinned down and held accountable for mistakes. However, exhausting/pedantic research on journey times in the books by some of us on the Westeros forum showed that the distances do track if you use the Wall as a scale bar, so he changed his mind on that point.
This size does seem to track pretty well. It means the North is about the size of Scandanavia, the Reach is about the size of France and Dorne is about the size of Italy (actually slightly larger than Italy), all of which seems to work.
And yes, there are five large cities in Westeros: King's Landing (pop. c. 500,000), Oldtown (c. 500,000), Lannisport (c. 300,000), Gulltown and White Harbour (about 50,000 each). The next tier of towns - Duskendale, Stoney Sept, Barrowton, Tumbleton, Sunspear's shadow town etc - all seem to be around 20,000 at the absolute upper maximum. The solution to the population problem - we've estimated that the total population of Westeros cannot be much less than 30 million otherwise the size of the armies doesn't make sense - is that there's simply a lot more of these second-tier towns than we've heard about so far. Barrowton, for example, is shown to be a reasonably big town in ADWD when we'd barely heard of it before.
This world map - which I recently assembled out of some newly-released materials - has a scale bar which may prove useful.