[Miller]

Is it the school name then principal?

ABC Elementary School
Mrs. Jane Doe
1234 Main Ave.
Xyz, LA 12344

or should I just do the principal's name and no school name at all?

[teachnkids]

I would do one of two things:

Principal name
School name
Address

OR

School name
Address
Attn: Principal

[ABusyTeacher]

I would do the way you have it listed. School name, then principal's name, etc. I figure that makes sure it gets to the correct building, then once inside...to the correct person.

[ZipLine]

Principal's name first. The school name and street address will ensure it gets to the right place.

[teachlife]

Always work backwards, start big and get small (state, city, street, building, person) is what I was taught. I'm sure it will get there however you do it
Mr. Principal
ABC School
1234 Student Dr.
City, ST 112233

[GraceKrispy]

I agree with either
Principal
School
Address

OR

School
Address
Attn Principal

[TraddStLovely]

In looking at several school websites, the expectation seems to be:

Name of Principal
School
Street Address
City, etc.