I took my Mum and we stayed at a perfect little hotel called Le Regent Hotel, 61 rue Dauphine, 75006 Paris. www.hotelleregent.com.
It's in the latin quarter and you could walk to the river, to the Louvre and to Notre Dame. The Louvre has buses to everywhere going from the front, so we hopped on one there to take us up to Sacre Couer.
We caught the bus from near the hotel to take us to the Eiffel Tour on another day.
We didn't eat breakfast in the hotel as there was a fantastic PAUL (bakery/patisserie) a few yds down the road, so we went there each morning and then bought a pastry to take out with us for morning snack!
Lots of restaurants nearby for the evening, lovely wandering streets, and interesting shops. Books, antiques, quirky things.
The other good thing about that area is you can get the train straight down from Gare du Nord to St Germain.
Remember if planning on going to Eiffel Tower, go first thing, the queues are big! Perhaps go for when it opens and then have breakfast/brunch afterwards.
After the Tower if you walk back towards the Seine, you can get on a Batobus, that will take you along the river, you get to see some lovely sights and buildings from the river. For a longer/sightseeing trip you can get on one of the tour boats ie a Bateaux Mouche, where you get the commentary and they are much bigger. You could go on one of those and combine it with dinner. See Paris lit up at night.
The view from the top of Sacre Coeur is fantastic. The steps aren't too steep or scary for littlies or oldies! If you are looking at Sacre Coeur head to the left for the tower entrance. Around Monmartre are lots of artists, and paintings, and places to eat, good for a wander.