The Marais quarter is one of the oldest districts in Paris. Located on the right bank of the Seine river, it covers an area from Chatelet to Bastille. It is very appreciated because it maintained its authenticity. During the day, you can go there for shopping in fashion boutiques, find a great restaurant,have a drink in a travditional cafe, rest in the garden of the Place des Vosges, visit the Picasso museum or the Carnavalet museum. Note that the area of the Marais is also very appreciated by gay people.
To enjoy a lively evening even late in the night, you will find everything you are looking for around the Bastille place.
And if you love operas, you should enjoy the Opera Paris Bastille.