We stayed on the edge of St Germain. Very pretty. Close to Musee d'Orsay but walk across a bridge on the Seine to the Louvre/ Notre Dame.
The Louvre is massive, so you would need to plan which works you want to see to avoid too much walking. If it is impressionists you want to see the Musee d'Orsay is better.
As Lovage says above,Eiffel tower is a long walk from the Louvre/Notre Dame area so you would get a metro or taxi there (we found the taxis really reasonable) and batobus on the Seine back if you stay in an area close to these. Also check out the release date for tickets for the date you are going on the Eiffel Tower website and book online as soon as they are released or you will have to wait in a long queue. Make sure you don't miss the gardens of Tuileries and Luxembourg - lots of places to sit and people watch. We did a site early morning, Notre Dame opens at 8am for instance then a cafe and one of the gardens followed by another tourist visit. Don't try to do too much in one day and make sure you visit the wonderful patisseries. Have a lovely holiday with your mum.
I'd go for the Marais. It's very central and safe but a lot cheaper than the more touristy bits. You get proper shops for picking up things to eat, not-ludicrously-overpriced cafes, and you could walk to Notre Dame and the Louvre. The Eiffel Tower is always going to be a metro-ride away, I think. Also the queues are always extremely long, which might not be great if standing still for a long time isn't good for her. But if you go early in the morning, that can be less bad and I think it's worth the queues, especially if she's never been before. Last time I went at dusk and that was magical seeing the lights of Paris come on from the top.
A nice non-tiring traditional tourist thing to do is get one of the Bateaux Mouches boat rides along the Seine (or one of the other companies that do this - there are several). They have guided tours in english and you get a feel for the shape of the city without having to walk miles and miles!
My mum has never been to Paris, though it was one of the places her and my dad always 'meant to go' and talked about doing so. Unfortunately he died when she was 54 before they got round to it - before they got around to a lot of things.
So, I am taking her for her 70th birthday this november (though we are sharing cost because I can't afford it alone!)
Basically we're looking at our must-sees being The Louvre, Notre Dame and Eiffel Tower - full on typical tourist type break.
Also mum's mobility isn't brilliant (arthritis) so don't want to be sat on metro for ages - she finds strolling along fine as long as she can rest occasionally.
Given the above, does anyone have any suggestions of where to stay? Any help would be greatly appreciated - looking at maps on the internet is never as good as first hand advice!