I do like the Brooklyn idea, but I'd have to say that I don't think you'd see one single capital. The territories east of the proclamation line and south of Quebec would probably be reorganised as one single entity (with a Brooklyn or Philadelphia capital), with any territories outside run under the same sort of authority as Canada, until Quebec demands standing like the 'Brooklyn Parliament', and potentially those who settle in the Great Lakes region.
Heck, I fully assume that Britain would try and offload a mess of its debts over the Seven Years War to the Brooklyn Parliament - after which colonies west of the Proclamation Line would be allowed again.
After that, I'd say Montreal would do for Canada, and then a city on the site of OTL Detroit would probably replace Ottowa as capital for the Great Lakes (and North of them), New Orleans the capital of 'The Mississippi Region' (Basically the entire Mississippi watershed with some dispute on whether the Great Lakes region ends at the Mississippi and Ohio rivers, or further north and east), with another 2/3 going further west (something has to go on the border with Mexico, and something has to handle British Columbia).
Frankly, I think the divisions might work very well if/when the British rule of the Americas ends. Clear legal borders, with most of the territories having a coastal border (Great Lakes excluded).