The assumption that Nash might take less money for a more desirable franchise seems naive when you actually look at the numbers.
This is because these over-capped teams can only sign free agents via the "mini-" mid-level exception. Such a mid-level signing would pay Nash roughly $3 million per season for, say, three seasons.
Compare that to the Toronto Raptors' recent Nash offer (via ESPN's Marc Stein) of three years, $36 million.
Maybe Nash would prefer to live in New York, but is that preference worth $25 million? Maybe Nash would prefer to chase a ring in Miami, but is a chance at glory worth $25 million?
Keep in mind that Nash left his buddy Dirk Nowitzki because Mark Cuban got stingy with the offer sheet. Nash may have been "loyal" to the Phoenix Suns, but such loyalty had the convenience of paying rather handsomely.
Of course, if he signs with Toronto, other factors will be cited.
He's a national icon, he could possibly work in the front office post-retirement, etc. Just know that the dollars, be they Canadian or American, will be the primary motivating factor.
My personal opinion is that the Portland Trail Blazers are the best fit for Nash, on account of how LaMarcus Aldridge's game meshes perfectly with Nash's pick-and-roll surgery.
If the Blazers want Nash, they'll have to pony up just like the Raptors did.