If you did the Bateau Mouche in the evening you could catch the Eiffel Tower all lit up and sparkly (on the hour, every hour). That would also cross off the insistence on "seeing" the Eiffel Tower, if there is one. I wouldn't actually go to the Eiffel Tower itself, there are far nicer bits of Paris.
Perhaps Montmartre? You can come out at Abbesses metro with its classic Guimard entrance, walk along the road, then take a funicular to the foot of Sacre Coeur. Feels very pretty and Parisian (shouldn't be too crowded in January) yet compact. Lovely views, including- yes- the Eiffel Tower, if you walk around the hill to the right a bit.
The Ile de la Cite is also lovely, compact, full of all kinds of interesting things, and right in the centre of the city (you can also get a sightseeing boat from there- the Vedettes du Pont Neuf). Obviously Notre Dame is a no no right now, but there are some really interesting illustrations on the hoardings showing the rebuilding work. And you could cross over the bridge to the Ile St Louis for ice cream at Berthillon, or over to the Left Bank to check out the childrens' books at Shakespeare and Co.
The Jardin des Plantes is just the other side of the river from the Gare de Lyon- it's my favourite park in Paris.