Best area to stay-Mother/Teenage daughter trip

No, there isn't a best area. Any central Paris arrondissement will suffice. Figure out what you want to see and stay in/near that area.

Recently I've been going back through threads about Paris hotels on this forum since I plan to go there myself (though probably not in 2018). There seems considerable agreement that the 4th, 5th and 6th arrondissements are convenient for a lot of first-time visitors, but that other locations not terribly far from Notre Dame can be fine as long as you are near one or more Metro stations.

Paris has sights scattered all over, but with only 3 days you'll need to be selective. So print a map off the internet (if you don't yet have a guide book) and mark the places you think you'd like to see. Perhaps you'll find that many of the things you hope to see are concentrated in one section of the city.

Amr,
My daughter and I enjoyed our stay at Hotel Diana within steps of the Cluny Museum. The hotel is conveniently located near a Metro stop as well as some bus stops. We took more buses because we thought it was more fun to see where we were going.
Enjoy!

Edited to add...
You don’t mention when you’ll be going to Paris but make sure to book your Eiffel Tower tickets up to 3 months in advance!

Most of the sites people come to visit are an easy stroll from hotels in the 4th 5th or 6th near the river; for outlying locations like the Eiffel Tower or Montmartre it is easy to take the metro. With only 3 days the key will be to be selective and prioritize what you really want to do.

Since it's a girls trip why not stay at a hotel themed on the lives of famous French women? It faces the Pantheon and is just up the street from Luxembourg gardens in a quiet area of the Latin Quarter. I've stayed there a couple of times and have been VERY happy...it's a classic Parisian boutique hotel. Metro is just a couple of blocks away so easy access to everything.
Hotel Les Dames du Pantheon

For a short visit it makes sense to stay as others suggest , 4 th 5th or 6 th , closer to river than farther .

I will even go further and suggest that you will likely enjoy the 6 th more than others .

I have stayed in all of them , plus several other arrondissements and all are good however .

I have stayed in the Hotel Diana - and agree it's a very good choice , for a few more dollars you could look at Hotel Le Regent ( I took anfriend there for her first visit and she adored the area ) on Rue Dauphine .
And if you have a lot more money than me I would look at the Hotel Aubusson

I would suggest staying in the 6th arrondissement, because Metro and Bus connections are very good, and you can walk to almost any place that suits your fancy. There's a lot to do in the 6th arrondissement.
I would stay in a hotel. It's too complicated to stay in AirBnB or other rental apartments.

You should familiarize yourselves with the Metro rules and regulations, ticket prices and so forth:
www.ratp.fr/en/plans-lignes?loc=reseaux&nompdf=bus_paris_geo&fm=gif

Download a map of Paris to see where the sights you want to see are located. Enter an exact address and the RATP website will take care of everything for you.

for a first and fairly short trip a hotel for sure. Our go to for short Paris stays is Henri IV Rive Gauche well located close to the river and the pretty square Viviani and quite close to Notre Dame. Small boutique hotel with small but nice rooms and the front ones overlook a picturesque old church. Very close to transport.