Make sure you get a large enough car. Even 'midsize' in Europe is not too big.

You did not mention how long you would be staying in each place. I would think at least 3 days in both VCE and Nice.

In London, Covent Garden, with the Punch&Judy show, and jugglers, etc. is enjoyable. All the standard tourist sites (wax museum, tower, buckingham palace, etc) are well worth visiting for first timers.

Skip the half price ticket line if the line is over 50-100 people long.

Some of the The Grand Canal Restaurants near the Rialto bridge are not expensive. Pick one that is not in the sun.