The answer is simple: cite, sight, site are homophones of the English language.
Keeping this in view, is it sight or site?
Sights is the word used for interesting places to see, often visited by tourists. Sites can be any place where something happened, or that is used for something (e.g. an archeological site, the site of the battle, a camping site). The phrase that is normally used is "sights to see."
Is it site or cite?
These three words all have different meanings, so it's important to keep the apart. Cite is to quote or refer to something. It is commonly used in academic settings. Site is a place or location that you can visit.
What a beautiful sight to behold?
a sight to behold. An especially impressive, noteworthy, or remarkable person, event, or thing; something or someone who is very much worth seeing. If you never go anywhere else in your life, make sure you see the Grand Canyon: it's a sight to behold.