I just bought a 2013 wrangler that has 35 12.5 on 20 inch rims, M/T Gladiators. It has 40 PSI right now and is pretty Loud driving, wondering if I need to lower the PSI and if it will drive better.

 

Most people will run a 35 closer to 28-30psi. The tire stores will always pump em up high cuz they don't know any better.

 

Generally, a larger tire requires less PSI for a vehicle of any given weight. Resharp001's recommendation is right in the ball park.
Do the old chalk test. Rub chalk across the tread, do a couple revolutions in the driveway and look for an even pattern across the width of the tire. Adjust pressure until you get there.
Don't have any experience with 20" wheels, but for 35 x 17 on my 4 door Rubicon I run 26psi.
Mine came off the dealer lot with 45psi (!!) and rode like a rock. It's common.

 

I looked up that tire and they don't advertise the typical load rating via a letter like we're used to seeing, but that is a 10-ply tire, and guessing with a 20" rim that sucker is likely "E" rated, so that sidewall is pretty stout. Probably not the smoothest riding tire on pavement, so y, 40psi is probably not too comfy.

**btw, tire pressure is always going to be a trade-off between fuel economy, wear and comfort. Technically nothing wrong with running 40psi, but the middle tread is going to wear faster and it's going to be rougher ride. Take em down to 28psi and you're creating more drag, so worse fuel economy but more comfy. Just stating the obvious here.

 

I have always found 30 psi to be a good starting point for larger tires on a JK. As mentioned, a chalk test will help fine tune to get the best tire wear.