You've mentioned that you prefer outdoor hikes and bike rides but you've chosen three large cities in which to stay. What do you plan to do in Paris and Barcelona? and for Swtizerland, you don't mention the mountains, just a large city?
You have 11 days.You've said 4 days Paris, 3 days Barcelona. Does this include your arrival day from the US? If so, that first day is going to be a blur due to jet lag. You can't count on getting much done on that day. That would leave three days for Paris. Four days in Paris is barely scratching the surface. I can't imagine only three days. Our first trip was 6 days and our second was 4 days. We still haven't done many things on our 'must see' list. However you get to Barcelona, from Paris or Geneva, it will take a full 8 hour day by train. That's one day of 11 gone. If you do add Geneva, that's another day or at least half day gone to travel as the train is 3-3.5hrs long. By the time you get out of one hotel and settle in another, your day is lost. You dont' mention the ages of your kids but if they're young, that 8 hour train ride is going to feel very very long. Your trip would look like this:
day 1 arrive to Paris. Jetlag on day 1. Sleep in Paris.
day 2-4 Paris (3 days to explore)
day 5 travelling from Paris to Geneva
day 6-7 Geneva (2 days to explore)
day 8 travel to Barcelona
day 9-10 Barcelona (2 days to explore)
day 11 leave for US
Two days is barely time to see anything. If you must choose two destinations so far apart, I would not add another stop. Just spend more time in Paris and Barcelona. If you really want to hike, maybe just do Paris and the Swiss alps (not Geneva). Its only a 3 hour transfer from one location to another and it would give you two very different locations.
