Favorite restaurants, everyday/elegant in London Paris Venice Florence Rome

We're exploring sites & places to eat by neighborhoods so if it's not too much trouble, please include the Arrondissement or neighborhood of your recommendation as I'm still trying to learn the areas. Also, please list your favorite museum, church or favorite place to visit near your restaurant suggestion. We are staying near Kensington Gardens, the Eiffel Tower, Ponte Vecchio, San Marco and Trastevere in the following cities. Might also go to Barcelona if we have enough time. Lunch budget $30-$80, Dinner $30-$200. Open to suggestions from everyday, romantic, adventurous, family-run, elegant styles of dining. Thank you in advance for your replies!

Source: http://www.fodors.com/community/europe/favorite-restaurants-everydayelegant-in-london-paris-venice-florence-rome.cfm

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