I have stayed in a hotel in Paris called Hotel Des Mines. I travelled alone with my 14 yr old son there two years ago, this past June my husband took our next son, now also 14 to the same hotel.
It is clean, very clean, the rooms are small, the location is very good, 15 minutes walk to Notre Dame, 10 minutes to Latin Quarter, and a metro stop just down the block. Plus a small convience store next door. Safe area, nice staff, and an elevator.
Costs between 60-90 euros, I actually paid 60 euros as I went in August which is a slower season then hubby who paid more as they went in June( very high season.
There are lots and lots of cheap( under 100-110 euros) hotels in Paris.Check out some of Ricks own suggestions, all seem pretty decent.
For a first timer I would stay in 5 or 6th arrondissmonts, Rick seems to favor the Eifel tower area, but area south of ET is pretty quiet and out of it,fine for a longer visit, but you only have 3 days.
Ps. Three days in Paris is too short!