When you say "I have to leave the hotel by 10 am.", is it wrong to say "I have to leave there by 10 am."?

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-I would say that both sentences are correct. If it’s a question of which one is more correct/ natural sounding than the other, it probably depends on the situation or conversation.
- The first sentence specifically mentions “the hotel”, so there is no ambiguity as to the place from where you need to leave by 10am. For example, it would be good to be specific like this if you are telling someone FOR THE FIRST TIME about having to leave the hotel at a certain time or YOU WANT TO BE CLEAR from where you need to leave by a certain time so that there is no confusion.
-The second sentence uses “there”, which is less specific than the first sentence.
Generally, I would use this if 1) I was having a conversation with someone, 2) I already mentioned the hotel earlier in the conversation and 3) I was not physically in the the proximity of the hotel.
If I was chatting with someone about when I need to leave the hotel and I was currently in my hotel room, then I would probably say “I have to leave “here” by 10am” (and really, you could leave out the “here” and the sentence would be fine or insert “the hotel” in its place).
Another example: 1) I am on vacation, 2) I am outside the hotel, maybe at a restaurant with friends. They asked me about my plans for the vacation and I could say, “I was planning to sleep in at the hotel tomorrow, but I need to leave there by 10am, otherwise I will be charges for another day’s stay”.

Overall though, the “there” to me acts as an emphasis word, something that is not necessarily needed for someone to understand what you are saying.
Hope that helps ☺️