I'm afraid, if you are looking for a rule, you may not get one especially when it comes to having the article before some monuments/buildings.
Articles are annoying! And, for some topics, you just need to learn them as they are practiced. And, that's it! You just touched the topic which should be learned as you read more and more authentic sources.
When it comes to buildings, it is more difficult to see a pattern emerging. It is more a case of Learn It. Compare the following:
The Eiffel Tower and the Tower of London are two landmarks in the capital cities of France and Britain.
If you come to London, be sure to visit Buckingham Palace, Westminster Abbey and the Houses of Parliament.
Where's Charing Cross station?~ It's off Trafalgar Square, between the Post Office and Coutts Bank in the Strand.
So, when recently Zuckerberg visited India, he did visit The Taj Mahal (Ignore the headlines, it does not have the article because of 'headlinese')
And, it is The (Leaning) Tower of Pisa.