Tchaikovsky is fantastic, but if you are talking about his Album pour la jeneusse op 39 it's quite difficult for a beginner.
You have plenty of stuff for that level. You could have a look at some syllabus, where you can find the pieces by composer and by level.
Burgmuller's op 100, lot of fun
A. Gretchaninov, interesting miniatures for children
C. Gurlitt, Heller, Streabogg also wrote lots of pieces for beginners
A. Tansman wrote several books from 1 to more advanced levels, short nice pieces.
William Gillock, who was a teacher, wrote lots of pieces for his students, really nice stuff.
Walter Carroll also a teacher, wrote some miniatures for piano.
A very interesting web to look for pieces, is this by the university of Iowa. They've have hundreds of pieces sorted by difficulty
https://www.youtube.com/user/UIPianoPed