I plan on buying Rally 1 rims for my 65 gto. Now have 14x6 rims with poverty caps. Looking at 15x7 rims in rear and 15x6 in front.  What is the widest tire that would fit in the rear?  

Are the offsets stock on the Rallye rims? If so, you'll be somewhat limited.

When you ask widest, you need to consider height (sidewall) also. That will dictate a lot.

Considering everything stock, 225/70R15 front is a taller tire. However, it fills out the wheel opening.  That would be a little taller than stock but would fit the 15x6 front rim. 15x7 in the rear would get about an inch taller and wider in the back without creating that "bowed out" look when the tire is wider than the wheel. One important thing to remember, every manufacturer tire size is not the same. A Goodyear tire vs. a Firestone tire in the same size may be slightly different. If you go to tirerack.com and click on the specs under the tires you are looking at, they give you a whole host of measurements including the recommended wheel sizes.