I think (b) is the suitable choice. But, I'm not sure. I also cant tell why (d) isn't suitable. Thanks in advance.
I'm sure you meant:
I think (2) is the suitable choice. But, I'm not sure. I also cant tell why (4) isn't suitable. Thanks in advance.
You are correct that (2) is the right choice. We use "either" when there is a choice between two things. You didn't ask about (1) and (3), so you must already be aware of the problems with them.
Now, given that you have two very fine hotels available for your holiday, would you be more likely to say, "we can spend time at either of them" or "we can spend time at each of them"? "Each" implies that you want to spend part of your holiday at one hotel, then move to the other. Moving from hotel to hotel is not how I prefer to spend my holidays.
By the way, I appreciate the effort you put into presenting your question.