I'm Lucy, and I'd be happy to answer your questions today. I'm very sorry to hear that this happened.
When a person rents a certain type of hotel room at a certain rate, that creates a contract. They were legally obligated to give you the room you paid for or one that was equivalent. If they didn't have another balcony suite available, then they're required to either refund the difference in value between what you paid and the room you got, or give you a better room. You can sue for the difference.
Breach of contracts cases unfortunately do not allow pain and suffering damages, so they will not have to pay extra for ruining your vacation. But they do have to compensate you. Since this is a luxury hotel, if they have a national customer service office or a regional manager, you may be able to get them to give you more of a refund, or a free night to be used at some later date, as an apology for what they put you there (or, if you're still there, you could potentially get them to give you something else - a meal at a restaurant, a gift certificate for the spa, etc.). Those are customer courtesies that aren't legally required, but things 5-star hotels will often do as a way of fixing problems and encouraging customers to come back (plus, they want positive reviews online).
Note that if you do wind up suing, it has to be in a state where the hotel does business, which means you could benefit from working it out with the hotel. When someone has to travel to receive compensation for a lawsuit, they unfortunately do not get compensated for their hotel and airfare. So that's something to keep in mind when talking to them. You could also try having a local attorney send them a letter if they're not responsive when you talk to them personally.
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