For your first-night meal, I’d add Oyster Club on rue de Jouy to your short list…. oysters, of course, but also other fish dishes on the short menu… usually a very enjoyable 20- and 30-something vibe, a mostly local clientele, light and airy space, engaging and personable service (at least in French), lighter meals perfect when travel-weary. The only minus (for tourists, not me as a local) is the lack of those bistro clichés and setting that many foreigners find so appealing.
The rue Jouy also has other possibilities: Vingt Arts et Vins, very artsy crowd, live entertainment (poetry readings, live jazz, etc) on some nights, always a gaggle of very clued-in Japanese expats (an indicator of quality) but somehow also very Parisian, comfortable seating, food is above-average wine bar trad-ish but also modern French nosh, I like it as French-speaker but not sure if non-French-speaking tourists would enjoy it as much; and Nico, a small plates/ French tapas restaurant, usually but not always (the luck of the draw) very good bistronomique/ updated trad food, very enjoyable bistro ambiance, and mostly Parisian clientele… it seems your daughter would enjoy the small plates set-up. I should add that many of us locals avoid the 4th because it’s such a touristy area and so many places are aimed at tourists and suburbanites. But south of the rue de Rivoli/ rue St Antoine seems to me to have better restaurants and more Parisians.
I only go in summer so not sure what it’s like in March but the new-ish riverside park on the lower quais of the Rive Droite from the Pont Neuf to l’Arsenal can be very enjoyable… dotted with barge restaurants and bars, grassy areas for picnics, etc. FWIW, my fave resto here (for lunch) is Maison Maison just on the other side of the Pont Neuf… small plates/ French tapas, fabulous Seine-side seating and also a very small indoor space when the weather is bad… access via stairs down from the Quai du Louvre across from the place d‘Ecole.
I haven’t been to Le Trumilou in years so can’t comment on its current quality. I have no experience of Nulli but my brother has good things to say about it and, if it reflects the quality of its older and very expensive sibling on rue Richelieu in the 1st, it will be very good indeed. But my brother offers one small caveat: Nulli is a wine-bar with food and, in somewhat usual wine-bar fashion, half the seating is stools at high-tops… if you can’t get a conventional table and chair, it could be an uncomfortable meal for your first night.
We all have our own tastes and preferences. Usually, I love street markets but am not a big fan of Marché Bastille on boulevard Richard Lenoir on Sunday. For me, it’s just too big, crowded, has lost its neighbourhood flavour, has become a bit of a zoo, a magnet for scammers and pickpockets (finding out exactly where “un pigeon” keeps his/ her wallet is easy in a market setting). On Sunday (as well as Tue to Sat), I much prefer the Aligre quartier (market street, street market and high-quality covered market) in the 12th, a 10- to 15-minute walk from the place Bastille or a short hop on the #86 bus. The area is also an excellent restaurant district and one of the very few quartiers in Paris where I would risk restaurant roulette. There was a recent thread about the Aligre quartier that will you give you more specifics on the area.