London - Paris - Italy- Zurich - What is feasible?

My daughter and i are heading to Europe of FF miles. I land in London will spend 2 nites and then head to Paris for 4 days. Need to fill in the blanks on the remaining 6 days before we hop a flight from Zurich. Need help deciding how to fit in Rome or Venice b4 we head home.A friend is telling me to fly to rome via a local airline another to drive... HELP!