Yep. I got 265 70 R17 and only had to remove the mud flaps. Now there is a difference if you get an all terrain tire versus a road tire. The road tire you should have to do no mods. However, all terrain is a bit wider and it will rub your cab mounts a bit. You definitely have to remove your flaps.
I've got a 2013 tacoma also. I just purchased a Kobalt tool box at Lowes for under $160 and it looks great. I painted mine black using Krylon primer & paint hammered spray paint and it turned out great. Just lightly sanded surface with 400 sandpaper prior to. You have to get a mounting bracket...