I'm going to take a contrarian view, even though the pics do show the killer view of the Eiffel Tower from those rooms at the Westin Paris.
The area around the Westin Paris is super nice - Rue du Faubourg St Honoree and Place Vendome are the epitome of Parisian chic - so you and your daughter will have a lot of enjoyable things to do, merely by strolling those fabled streets.
I would take the $700 that you will not spend on the upgrade and book a table at Jules Verne, the Michelin one-star restaurant on top of the Eiffel Tower for a nice dinner. Now, THAT would be a memorable evening and a good use of your $700 - you will need every penny of it since the bill will be a shocker when you receive it
Start with a nice bottle of Champagne, then their ecrevisses and oysters, and go from there...