What are some great things to do "off the beaten path" in Paris and Rome?

What are your interests? And, how long are you in each city? ts difficult to find any peace and quiet in Rome in summer because of the number of tour groups. Something fun to do though which may be a bit less hectic is visit EUR, a sort of fascist suburb that Mussolini envisioned as the model for how things should look. Although he lost the war, the finished building EUR anyways and its really interesting--a few great museums, amazing architecture, and the "square colliseum", a sort of modernist version of the original. its an easy metro ride from the center of town and worth a visit if you go for that kind of thing. Something else fun is the neighborhood known as "Monti". Its by the Cavour stop on the Metro and its a nice place to walk around, good restaurants, nice shops and a great place to people watch. Its sort fo like what Trastevere was before it became so hip.
if you tell me more of your and your daughter's interests, i can point you in some other directions.