OK, here's the stuff my sister sent me.
She too does recommend visiting the Catacombs, as well as the Cluny museum ("the Middle Ages museum 'par excellence'") - it does show the "Lady and the Unicorn" tapestry -- assuming it has been restored, which she thinks it has.
The Louvre (the oldest part has been opened a few years ago, she says!) and Cluny have sculptures, jewelry, etc exhibitions, but she advises to check the programme to check on which days they are open (she believes they may be closed on Tuesdays).
She suggests that, for lunch, you head back towards the Halles and Rue Tiquetonne away from the Notre Dame area, which, though picturesque, will set you back a pretty penny.
The Conciergerie (early 14th century prison).
There are other sites you can visit, but you'll be getting further away.
The National Library has a collection of Louis XIV terrestrial globes (ok, that's somewhat later ) on permanent display.
There are plenty of private houses from later centuries everywhere, but you'll have to check with the Tourism Office (or Google?) for specific addresses.
Near the Chatelet and Beaubourg, there's the Tour Saint-Jacques (15th).
Near the Halles, the Saint-Eustache church (16th-Renaissance), the Fontaine des Innocents (oh, and the fountain on Place Saint-Michel between Notre-Dame and Cluny is nice too) and the Tuileries palace.
Nice areas to wander around in: Quai Saint-Micher, Boulevard Saint-Germain, Odeon, Beaubourg, Rue Tiquetonne (affordable good food), the Jardin des Plantes (been there recently, it's a nice break from being in a frigging city), Jardin du Luxembourg, Jardin des Buttes Chaumont (no monuments she can think of, but her favourite park), the Louvre, Jardin des Tuileries...
If you like contemporary art (she's an artist, can you tell?), you can go see Beaubourg, the Picasso museum, the photography museum and more...
She thinks you can get 1-day or 3-day passes which are cheaper than single tickets, which can cover multiple monuments/museums, but you'll have to check with the Office du Tourisme.
There, hope that gives you some more ideas.