I've never been in Rome at Christmas, but I have been to Paris for Christmas/New Year's 5 or 6 times, and it is LOVELY. For a wonderful food sampler experience I recommend spending a late afternoon/evening at the street market along the Champs-Elysees (see all markets here: http://tinyurl.com/knqf8gm) There are glittering lights, wonderful people-watching, and stall after stall of gifts and trinkets - and there's also stall after stall of FOOD, from saucission to amazing stewed mushrooms to warming soups, and you can walk along the street drinking hot mulled wine!
If you will be in Paris the 20th – 22nd of December, you might want to check this out: http://tinyurl.com/ncg76td
I quote: “The 'Noël Gourmand' trade show takes place from 20 to 22 December at the Palais Brongniart in the 2nd arrondissement of Paris. Three days of gastronomy showcase the talent and expertise of the best artisans in France with upscale products and regional specialities to discover. A wonderful array of farmhouse cheeses, regional dishes, oils, spices, mushrooms, seafood, salted meat, foie gras, wine, chocolate and confectionery ... to devise and prepare unforgettable Christmas and New Year dinners and seasonal festivities.”
I like to drop in at l'Eglise Saint-Merri (http://en.wikipedia.org/wiki/Saint-Merri) for a concert. They do wonderful music, and while it's right smack dab in the center of town at 76 Rue de la Verrerie it feels like a "locals" church. On one visit, we discovered a show by local artists, with amazing modern works hung up in this gorgeous Gothic church!
Pub suggestion is The Highlander, at 8 Rue de Never, a 15 minute walk - oops! a GORGEOUS 15 minute walk! - from Saint-Merri. It's an ex-pat joint, staffed by folks from the UK (mostly Scots) and is very cozy, welcoming, and friendly. I know everything thinks of sitting at an outdoor cafe in Paris - and you must! - but I always like to stop in at an ex-pat joint at least once while there. I get amazing tips on what's new in town, and where to eat off the beaten tourist track, for one thing. This bar is where we heard about Au Petit Suisse (http://www.aupetitsuisse.fr/) a cute, friendly, old brasserie that serves delicious food in a CLASSIC Parisian setting. It's right by the Luxembourg Gardens (also a 15 minute walk from The Highlander, but in the opposite direction).