Well, I see no one else is jumping in on this for you, but you'll want to choose plants that are silver or white, and some folks include black and blue as well. Some include those with moon associations, like moonflower or willow, and many include night-blooming/fragrant plants as well.

Good choices:
Moonflowers
Artemesias
Dusty Miller (annual)
White Cosmos (annual)
White roses
Night Blooming Phlox (annual)
Phlox paniculata, white varieties
Globe Thistle, Arctic Glow is white, but the blue is nice, too
Eryngiums
Brugmansias and Daturas (will need overwintered inside)
Liatris-white
Shasta Daisies
Centratherum rubra v. alba (white Jupiter's beard)
Valerian
Vervain
White Poppies (black peony-flowered ones look cool mixed in)
Boltonia
Bronze Fennel (lovely dark background for the flowers)
White Lilies
Scabiosa-blue or white
Buddleia-white or blue
Jasmine (will need to winter indoors)
Achillea ptarmica, sneezewort
Babies Breath
Nicotiana "Only the Lonely"
Echinacea "White Swan"
Campanula, white or blue
Dichondra "Silver Falls" (annual, this is the first year I've planted it)
White dianthus, or the white picotee annual variety, Velvet n Lace
Lychnis, white
I like the idea of hanging baskets in my moon garden, as well as bird feeders, so I use double shepherd's hooks for them. I like the drapey look of long vines in the hanging baskets, and petunias and other heavily flowering annual plants in the baskets.

HTH,

Celene

What a lovely idea for a garden. I think I will try one too and thanks for asking what plants to put in a moon garden. That list is wonderful. What an enchanting idea.

You've gotten a great list from Aunti Celine! One more plant to consider...Tuberoses. These are show well at night and really put out a beautiful fragrance starting around sunset. Bulbs planted in spring bloom in July here in my Tennessee Zone 6 garden. I dig them up right after the first frost and store them under the house in the winter.

Evening primroses (the stalk-growing kind, not the cup-shaped kind) are a pale shimmery yellow that look really good at night, especially near white.

Basic grape hyacinths glow in dim light. As a blue, that's pretty valuable. They're inexpensive, too, and if you put them in raised beds, you get to see them more, and the scent is up where you are.

White mophead hydrangeas will really make an impact in shade, and so will variegated-with-white hostas.

Here's one that I doubt many have ever thought of.
It is the White Top pitcher plant - Sarracenia leucophylla.
Though a wetland full sun plant during the day, it is incredible in the moon. The Harvest Moon and again in Oct its at its best depending on location. Because the largest pitchers are produced during the late/ early summer autumn.
When mature these insect eating plants produce some very impressive 3' tall pitchers that are illuminated in with moon light, almost like a light is inside the pitcher, a strong glow. The reason for this is that the plant lures moths to the glowing trap, they are a major part of the diet in late summer and fall. To prevent bug capture as it will cause the pitcher/leaf to not last long a piece of cotton can be placed inside the pitcher opening (though it will hamper the glow at night)

During the spring and early summer the traps are smaller and though still interesting in the moon glow, this time of year they are incredible. In the spring the pitchers may be smaller but the beautiful large deep red flower is another show on its own hanging upside formed like a umbrella.

These plants are hardy from USDA zone 5 through 9, and are found native to the gulf coast of the deep south in bogs.

Check these plants out, I promise after you have a few mature ones in your moon garden you will be very impressed.

Take care,

Mike
St. Petersburg Florida