Just to make it clear, when Columbus reached Hispaniola, he had already first landed on several smaller islands of which we are unsure of which exactly, and then coasted and landed several times on Cuba.

His landing on Hispaniola happened on the very north east of the island, in a bay he named Puerto de San Nicolas translating into Port of San Nicholas as he landed there on 6th of December, St. Nicholas Day. Link to the first voyage log which talks about it. .

The bay, and the town near it, are today called Môle-Saint-Nicolas which is basically the French version of it. I have no idea if they have any monument of the event, sorry

Columbus then proceeded down Hispaniola coast, suffering a shipwreck on Christmay day of his ship Santa Maria, forcing him to leave around 40 men of the crew in a makeshift settlement named La Navidad (Christmas). The men left all died before the Second voyage arrived, dying from diseases, infighting and fighting the local tribes.

Here is one version of what we think was Columbus exact route but we aren't sure for some of the details, especially the island on which he first landed