Not good or classic but mine just saw High School Musical and loved it.

She loves sound of music and I want to show her Swiss Family Robinson.

Mine loved Back to the Future, Jumanji 2, and Aladdin.

I agree that the Disney movies are great. While the animated ones are best known, the live action ones are great too. Specifically recommend:
Mary Poppins
Escape to Witch Mountain (1975)
Bedknobs and Broomsticks
The Parent Trap (1961)
Pete's Dragon (1977)
Pollyanna
Freaky Friday (1976)
Honey I Shrunk the Kids
The Santa Clause
Princess Diaries
Sky High

Wikipedia has a list of Disney Movies. Generally, when they've remade the movies, I think the originals are better.
https://en.wikipedia.org/wiki/List_of_Walt_Disney_Pictures_films

Classic musicals are great too. Some are geared more towards kids:
Sound of Music
Wizard of Oz
Peter Pan
Annie
Chitty-Chitty Bang Bang
Shirley Temple movies
Danny Kaye
Willy Wonka and the Chocolate Factory

Non-kid Musicals:
Singing In the Rain
My Fair Lady
Music Man

Classic non-musicals are good too:
Laurel and Hardy
Abbott and Costello
Three Stooges
Cheaper by the Dozen (Dad dies at the end)

Animal Movies
Homeward Bound
Benjii
Beethoven
Black Beauty

Miscellaneous Movies:
Short Circuit
Galaxy Quest
Ever After
Charlotte's Web
ET
Ella Enchanted
Jumanji
Night at the Museum
Nim's Island
Hook (one of the Lost Boys is killed)
Princess Bride
Spy Kids
Superman (Christopher Reeve)
Star Wars
Three Men and a Baby
Flintstones Movie

Sound of Music, Mary Poppins and Mary Poppins Returns, Parent Trap (both of them), Freaky Friday, Mr. Peabody and Sherman, Mulan, Hercules, Mrs. Doubtfire

We really loved the Fantastic Mr Fox at that age. IT's quirky as heck, but it appealed to us.

We also really liked Megamind at that age.

Common Sense Media can be a long time friend to you. I love it and use it on a regular basis. It gives you post points, areas of concern, ideas for further discussion.

Heck sometimes I use it to see if I myself wouldd enjoy a move.

That said, their age recommendations skew a little conservative for me, but I know that and I read what they say and make my own decisions.

You're at prime Disney age. There are some great ones. The Lion King is a fabulous animated movie, looks like the new one is not getting the same rave reviews.

Home Alone

Princess Bride!!!!!

Pollyanna, Sound of music, my fair lady, Shirley temple films, parent trap (mine also loved mary poppins).

Annie, ET, Escape from Witch Mountain, Mary Poppins.

Ours adore Mary Poppins.

Whale Rider.

My son loved all the Free Willies.

I'd love to start a family movie night tradition with my 6 year old. Any thoughts on good, classic movies for that age?

She loved Karate Kid and Black Stallion