Paris is one of the reasons many people visit Europe and for good reason.
You will see the Eiffel Tower, the Louvre, the Seine, and nearly every other famous place if you spend only a few days here. Montmarte is a cool young place to stay, which is where my hostel/hotel was located, so I recommend this area. Rates are also lower in Montmarte and in other districts than other neighborhoods in Paris, so check before you book. Getting around by the metro is so easy you don’t need to spend more to be in a central location unless you really want to.
There is an undercurrent of romance in Paris, especially at night. In Paris, there is something for everyone, so while it is a bit more crowded and packed with tourists, at the very least, a day-trip to Paris is a good idea.
All opinions are my own.