Cllimate is the biggest determinant of biomes, so if you want to get your biomes right, it pays to figure out your climate first.

Grasslands are largely driven by moisture. The Great Plains are grassland because they lie in the rain shadow of the rocky mountains. Farther east, moisture comes up from the Gulf of Mexico to allow for forests.

The Arabian Desert is created by the subtropical high -- a band of high pressure that sits at about 30 degrees N and S latitude. That's the same as the Sahara, Sonoran, Kalahari, and Australian deserts. You would expect to have deserts at about that latitude all around your world.