When I bought my jeep from my dad it had 31x10.5s on it and it looked pretty good IMO. Fast forward 2 years and I'm in the rabbit hole of trying to run 33s the right way. (Please don't hate for the Patagonia's Purchased before seeing all the disapproval in this forum )
Put on 31s (they will probably rub a bit at full lock), and get a cable shifter for the transfer case (Everyone should have it). Drive it like that for awhile. If you aren't on difficult trails or offroad at all for that matter the 31s will be great and you won't break the bank.
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Our LJ is stock with 31's. It's a fine ride and an excellent look for a Jeep that totally LARP's and never leaves pavement.