Dolphin VR

Dolphin VR is a branch of the Dolphin Emulator which lets you play Gamecube and Wii games in Virtual Reality. It's rather old at this point and takes a lot of fiddling around, and the results aren't going to be ideal as these games were never meant to be played this way, but with enough work select games including Mario Kart Wii play surprisingly well!

It should be noted though that you will almost certainly want to have your "VR legs" so to speak prior to using Dolphin VR as it can be a rather intense VR experience that's not recommended for beginners due to the game's low refresh rate (well, low for VR) and camera movements not designed for VR.

Settings

Download the latest version from here: https://dolphinvr.wordpress.com/

Yes, the latest download is from July 2016. There's a myriad of reasons why this is the case involving distribution licenses and feuds, but long story short, this is the version you'll want. It's based on an old version of Dolphin so it'll be missing a lot of newer features.

In order to play smoothly, we'll need to adjust a number of settings. Each section will be dedicated to one of the settings buttons found at the top of the main Dolphin window. I'll include screenshots of all of the settings I'm currently using along with some notes about specific settings.

Config

Below is a screenshot of my settings.

I don't know if setting Deterministic Dual Core to fake-completion is necessary depending on your processor.
Technically base Mario Kart Wii should work fine with CPU Emulator Engine set to JIT Recompiler (Recommended). However, in my experience LE-Code distributions would not load unless I used the JITIL Recompiler. At least in my case (first with an i7 6700 processor and now an i5 12400F) this didn't have a noticeable impact on performance.

Graphics

These settings are optimized for using a higher resolution texture pack. If you don't want to use a texture pack, disable "Load Custom Textures" on the advanced tab.
Note that checking "Prefetch Custom Textures" can cause a long period of massive slowdown after you press start on the title screen and open the main menu. It should stop once all textures are loaded and is still recommended if using custom textures since prefetching prevents slowdown mid-game.
Some tutorials note to use OpenGL as the backend but this caused an awful strobing effect when I tried it so I stuck with Direct3D11
For best performance, uncheck Scaled EFB Copy. This makes a huge difference in regular Dolphin, but in Dolphin VR it doesn't seem to make any noticeable graphics change to have it enabled but can cause major slowdown, especially with transparency effects.
You do not need to set the stereoscopic 3D Mode as it should automatically configure itself when you boot your headset.
There will be some graphical glitches with these settings with UI and HUD elements, but from my experience they result in the smoothest performance of actual gameplay.

VR Tab

These will be highly dependent in your headset settings. I'm using an Oculus Quest 2 running Virtual Desktop primarily.
Free Look Sensitivity is extra low and will require some initial adjustment once in-game.
VR Game contains some important settings, but we can adjust them on a by-game basis so we'll ignore the tab on this menu.
If you're prone to motion sickness, the motion sickness tab has some options to combat it, but I haven't made use of them so I cannot vouch for their effectiveness.

Game Properties

Right click on the game itself and click properties to get to these settings.

The Units Per Metre settings controls the scale of the game world relative to the player. The larger it is, the smaller the game world becomes relative to the player. I got a value of 90 by comparing my height to the height of Rosalina (I'm 6'1" or 1.8542 meters tall, and I figure Rosalina is probably roughly that height as well), but if you feel it's off feel free to adjust it.

The three Hide Objects codes seen here were automatically included in my Dolphin VR install and I'm unsure how to find what they actually are, so unfortunately I can't help if they aren't included in yours.
I use an alternate method for hiding characters but if you don't want to do some editing of your iso (which is necessary for Mario Kart WiiMix anyways but not for regular Mario Kart Wii in VR), you can add the codes found here to hide Mario's head. This does have some side effects of hiding random other items as well though and Mario's body can often clip into view when you hop or trick.
I think the Disable Culling Outside Camera View was baked into Dolphin but in case you need it you can find it on this page.
Disable Culling Outside Camera View will force the game to render all objects at all times regardless of whether they're in view of the "camera" (or in our VR case, in front of our vehicle) or not. This can cause some strain on the CPU so I recommend disabling it if you have performance features. I'd definitely recommend using it if you want to try Battle Mode though.

Hot Key Settings

Hot key settings can be found in the options dropdown at the top of the emulator.

You will want to set bindings to your gamepad for Freelook Move Up, Freelook Move Down, Freelook Zoom in, and Freelook Zoom out. A binding for Freelook Reset is also highly recommended, although make sure you don't pick something that you might accidentally hit mid-race.
I recommend remapping the freelook options to the right stick since it goes unused in Mario Kart Wii. I mapped the view reset to one of the D-pad directions and remapped D-pad Up to left stick click in so I can wheelie and trick without taking my thumb off the left stick, but do whatever works for you.