Will putting 17' rims affect my '08 FJ Cruiser that comes with 16' rims?

Larger rims won't interfere with other car parts, like brakes and suspension, as long as they are about the width as the stock rims. And when buying replacement rims, you have to get rims designed for the car or they might not line up with wheel bearings, and that can cause problems..... But it's not the rims you have to worry about; it's the tires. If you go with tires that are much larger than the stock tires, it can change the car's handling, steering, ride, transmission shifting, and might encroach on fender wells and other things. Also, you'll have to keep in mind the difference in the car's speed when you drive. With larger tires, the speedometer might show seventy mph, while the car's going eighty.

Not much more I can add to what was stated above but remember when you increase mass or drag from larger tires and rims fuel mileage can drop cause it take more energy to turn the tires.

Why not just go to the largest 16” tire that won’t negatively effect all the above mentioned ?