A combo of your overall diameter and wheel offset is what will affect your clearance. I know that on a 22x9 with a 32mm offset, a 31.6" tire will not rub at stock height. I would assume you could run atleast a 32" tire on the same wheel, which would be a 285/45/22 Terra Grappler. If you don't want to do any trimming, that would probably be your best option. However, a 305/45/22 is only an inch taller and roughly 1/2 inch wider.
A lot of people on here say they had minor trimming with 33" tires on roughly stock offset wheels even with a 2.5" leveling kit. In my opinion, I had minor trimming with a 34.3" tire with a leveling kit. Everyone's opinion of trimming is different. My father inlaw has a 2010 Tahoe and didn't even notice that I had trimmed anything until I pointed it out to him and showed him the differences on his Tahoe compared to my Yukon. If I was going to need a lot of suspension movement (offroading), I would need another 2 inches of lift just for clearance when turning.