I love the 7th Arrondissement. When we lived in Paris, this was our neighborhood and we visit several times a year and stay here. As for hotels, I recommend Hotel Relais Bosquet at 19 rue du Champ Mars which you can find out about at www.hotel-paris-bosquet.com and Hotel Muguet at 11 rue Chevert which you can check out at www.hotelparismuguet.com . Both are lovely, comfortable, and have friendly staffs. Both are, of course, air-conditioned and quite charming. The Hotel Relais Bosquet also rents out some apartments (click "our apartments" at the bottom of their home page on their site).
Why the 7th? It is very close to the Eiffel Tower, my beloved Musee d'Orsay, the Musee Rodin, the Champs de Mars gardens, the Invalides, and to the Rue Cler area. You can get anywhere from here using the Metro and buses. It is the Paris people dream about, beautiful architecture, wine shops, cheese shops, chocolate shops, veggie and fruit markets, flower stalls, bakeries and cafes, good restaurants, boat tours on the Seine, and more. If you ever read Ludwig Bemelman's children's books about Madeleine, this is the area of Madeleine's magical neighborhood. You will feel like you live in Paris if you stay here.