I've never heard of a 270/70r15 but if it exists it's going to be tall and skinny compared to the tire you have now. The 255/60r15 was the upgrade size from the factory 225/70r15 tire. You might be thinking of a 275/60r15 which would be the next size taller and wider from what you have now. If your looking for wider than you may want to look into a 50 series. If they still make them I used to sell 265/50r15, 275/50r15 and 295/50r15 for the fat rear tire look. We did have a 305/50r15 and I believe a 325 followed shortly thereafter.
The wider you go it's possible you'll need a wider wheel and you'll have to check for clearance against the emergency brake cable and frame. Due to cost and availability most of us have switched to 17 or 18" wheels to get the look that makes these cars come to life, depending on your preference
A great tool I've used and recommend is this tire conversion calculator where you can put in your current tire versus a tire your considering and you'll see how they compare in height (aspect ratio) and section width.
http://www.miata.net/garage/tirecalc.html
