Hi, Jason! I've already corrected your homework. Here are the corrections:
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I'd like to go with my family to Gyeong-Ju City, where is the Capital of the Silla Dynasty in one thousand years ago. There are many ancient architectures in Gyeong-Ju city. For example, Bulkuk Sa temple, statue of the Buddha made of stone and an Observatory called as Cheomsongdae. They have been very preserved. The city is historically famous one, which is very educational for my children.
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Correct:

I'd like to go with my family to Gyeong-Ju City. It is the Capital of the Silla Dynasty in one thousand years ago. There are many ancient architectures in Gyeong-Ju city. For example, Bulkuk Sa temple, statue of the Buddha made of stone and an Observatory called as Cheomsongdae. They have been welll preserved. The city is historically famous one, which is very educational for my children.

Explanation:
*You can make your first sentence into two sentences. You should put "it" instead of where to indicate that you are starting another sentence. Instead of putting "very", the word "well" is much suitable to describe the places. You can omit the word "one". It is no longer necessary in your last sentence.  

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Thank you very much for doing your homework, Jason. I'm glad that you are able to write a composition out of the homework I gave you. You also had minor corrections. Keep it Up! See you soon in class. Take Care~

~T.Cherry:)