Off season Paris is ideal for taking in its museums. It’s your best chance to see Versailles and not deal with hours long wait times (though early/late in the day is still advised.) Marais is my preferred neighborhood with a nice atmosphere, but not far off from everything. There’s good Airbnb’s in this area as well. The key is to be near a Metro stop. You can get anywhere in Paris within minutes using the Metro, and don’t be deceived Paris is BIG. Outdoor stuff might be dicey, but a walk and or boat ride on the Seine is great any time of year.
For off the beaten path sights, I’ll usually recommend Opera Garnier, Musee Jacquemart-Andre, and Marmottan. Food-wise, Paris is one of the places where I’d rely on guidebook and local recommendations. There’s just so many places to eat, and you might end up fat from where you planned sometimes. My only recommendation is Le Grand 8, up in Montmartre. It’s worth the trip up there, and nice to walk around after.