The NZXT H700 would be a good choice, comes with 3-120mm intake fans in the front and a 140mm fan in the rear as exhaust so with a 360mm AIO I'd mount it on top as exhaust. I have the H500 and there easy cases to work in and cable management is simple and looks great.
PCPartPicker Part List
Case: NZXT - H700 (Black) ATX Mid Tower Case ($137.59 @ Amazon)
Total: $137.59
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2019-05-03 15:20 EDT-0400
If you want something a bit flashier I'd go with the Lian Li PCO-O11 Dynamic. With it's dual chamber design it keeps the PSU/cables behind the case while the front is showcased in glass. Like the H700 I would mount the AIO on top as exhaust but with this case I'd put 3-120mm fans on the bottom (with filters) as intake as well as the side fans (3-120mm) with intake. For fans you could go either RGB or non depending on preference. Just a heads up this case doesn't come with fans so consider that into the price.
PCPartPicker Part List
Case: Lian-Li - PC-O11 Dynamic (Black) ATX Full Tower Case ($130.27 @ Walmart)
Total: $130.27
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2019-05-03 15:24 EDT-0400
There's quite a few other options that would support that 360mm AIO but if this is for a gaming system you'll want to setup the AIO as exhaust as not to dump hotter air into a already warm system considering the GPU.