Suggestions / Fitment Issue

These tire sizes confuse me and thought I would get some help from you guys who know this stuff in and out. I currently run a 265/75/16 tire on my 2006 DCSB TRD 4x4. My truck has no lift, but I'm hoping to add a little bit bigger / more aggressive tire shortly. My neighbor runs a 266/65/17 General Grabber AT2 which is nice and more aggressive. Will this fit? If so, any other tires / sizes I should consider? Most of my time is around town, not much on the highway. I spend about 2 days a month on the trails for camping, but not time off road all things considered.

 

the equivalent to a 265/75/16 is a 265/70/17 both 32s