For me, if I can find something inside a ten to 15 minute walk to Notre Dame (I use that as an indicator of THE center of Paris), I consider it ideal. For that reason, I really like the Marais and the Latin Quarter (4th, 5th and 6th). They are nice areas and very convenient. Being 20 minutes walk to the Eiffel Tower means you will always use the metro to get around. From the Eiffel Tower to Notre Dame is I'd guess still well over 30 minutes walking. I've never walked that far but I did ride a bike from Luxembourg gardens to Eiffel Tower and it was a little less than 30 minutes. I can't describe how nice it is to take a ten minute stroll through older areas, or along the Seine, to get where you are going; especially during the rush hour parts of the day on the metro.
I think you can tell a place's location by the postal code. If it ends in 004 for example, it's in the 4th. I believe that pattern holds for all the arrondissements. What I normally do is place it on Google Maps to see where it is. You can also use Google maps directions to guess walking times. For instance, Google maps says the walk from the hotel you mentioned in the 15th to Notre Dame is 1 hour 7 minutes.