As for places to go, since you won't be there very long, take one of the half day tours of the City so you can see highlights of all the sites. Then you'll have more time for other stuff. Since you will be there on a Sunday, none of the stores are open. I'd recommend you visit the Marais, which is the old Jewish quarter of Paris. All the boutiques there open in the afternoons on Sunday. To get there take the Metro to the St Paul station. Exit there and walk up rue Pavee to Rue Rosiers. Turn Left onto R. Rosiers. Also on that block is a fantastic falafel place.
I would also recommend you visit the Angelina tea room on r. Rivoli near the Louvre and Tuilieries. They have yummy hot chocolate.