Outside:

Green hills, a vast ocean and some far off islands.  And the usual cloudy sky.

Bob-omb Battlefield

Same as outside.

Whomp's Fortress

Cloudy sky.  Jolly Roger Bay

Rock cliff wall, sky which looks overcast.

Cool, Cool, Mountain

Snowy mountains, dark sky with clouds, snowing all the time, darker mountains lowest in the background

Big, Boos Haunt

Dark, shadowy trees, with night sky( moon included) as well as a metal fence.

Hazy Maze Cave

Err, the inside of a cave?

Lethal, Lava Land

Sea of lava with sunset like background included dark clouds.

Shifting Sand Land

Desert Background, with clear blue skies, quicksand just before background and the sun.

Dire, Dire Docks

Clear sky, sea in background, tall, rocky cliffs.

Snowman's Land

Same as Cool, Cool Mountain

Wet-Dry World

Water like sky with a detailed town/city in the far background.

Tall,  Tall Mountain

Same as outside and Bob-omb Battlefield

Tiny-Huge Island

Same as outside.

Tick Tock Clock

The inside of a clock with roof  and black pit.

Rainbow Ride

Clouds

Total darkness, black background in other words

Bowser in the Dark World

Hard to explain cave like background.  See the background map.

Sunshine Isles

Same as outside

Goomboss Battle

A dark, eerie forest with jagged trees, fog and a dull, grey sky.

Bowser in the Fire Sea

Same as Lethal Lava Land

Metal Cap Cavern/Behind the Waterfall

Same as Hazy Maze cave most sides, waterfall one side.

Vanish Cap under the Moat

Total black roof, grey walls and a bottomless pit for a floor.

Chief Chilly Challenge

See Cool, Cool Mountain

White Room

Totally white roof, walls and floor.

Over the Rainbows

Like Rainbow ride

Bowser in the Sky

Purple lower clouds, red middle clouds and blue/dark blue highest clouds.