Apple, what size tires would you recommend for these keystone rims that you have shown, 15X7 rims?  Thanks!

As Bruce mentioned, I'd have to say stay with a 70 series tire...anything wider than that is not gonna fit on the rims properly. If your 255 tires are clearing now, a 235/245-70 should be just aboot right.
I'm not a tire eggspert, so don't take this as gospel...

Thank you everyone for all of your great help!  I have an additional question. The original wheels I have on it now are 5X4.75" or 5x120.7.  I have found a nice set of 15X8J rims that are 5X4.50".  Would these work and can you please tell me what the 4.75" or 4.50" measurement actually means?  Thanks again to all of you!

That means the bolt pattern measurement. The holes are either 4 1/2" center/center, or 4 3/4" center/center. If you measure your rims, start on one stud, then to the stud 2 studs over from that. That gives you the bolt pattern of the rim.
Don't quote me, but I think Corvette used a 4 3/4" pattern...

There was a post here a while back that gave a link to a really good site that had all kinds of rim/tire info, such as how to determine backspacing, bolt patterns, etc. It's been a while since I've seen it...prolly a year or so.

Your Vette uses a 4 3/4" bolt circle. Those 15"x8" with a 4 1/2" bolt circle won't work. That fits Ford, Mopar, AMC, Studebaker and maybe a few more.