If you have the OEM class IV 6500lb hitch receiver, the spare tub gets pretty tight and you end up with right about 31.9 inches of clearance for the spare. I could not fit my 265/70/17 Pirellis in the spare location with the big hitch receiver, but I know people have fit other 265/70/17s in there. There are quite a few threads in this forum about spare tire size and all the different options between squeezing it into the factory tub vs a swingout or door mount.Did you have any issues with fitting the 265/70/17 in the spare tire location?
And yeah, my biggest thing with mods for now is I simply don't have enough experience to know where I want this vehicle to evolve, so I'd rather explore its limitations stock, and learn more about what I want out of it before diving deeper.
If you use a smaller hitch receiver or no hitch, a 265/70/17 should fit with little to no drama. I would still suggest the 265/70/17 size vs a 265/65/17 as I think it just looks right on a stock suspension GX. You also get the added bonus of a little extra clearance and likely a more accurate speedometer.