The larger tire will fit on the rim and will probably not have any
clearance problems. Lots of people run the 215 because the
availability is much better. I doubt it will have much effect on the
handling though one way or another. You actually end up with the
same amount of tire in contact with the pavement. Increasing the
width 10mm might have some marginal positive effect but it's
probably offset by the slight increase in sidewall height.

The general reason that wider tires are desirable on a car is
that a tire that has a lower sidewall has less flex than a higher
sidewall. So, you use a larger wheel and a lower profile tire.
But, lower profiles have less load capacity so you bump the width
to get back to a tire large enough to handle the load.  (In
general... a wider track width doesn't hurt.

Use this calculator to determine how much the speedo will be off.
Also, get the manual out and check the other stock sizes. If you can
find a stock size that is closer to your new tires, then you can have
the dealer set the computer to make the car think it is running the
other size and the speedo will be closer.

http://www.miata.net/garage/tirecalc.html