Paris, Rome and London are all “worth” 4 days; Venice and Amsterdam, at least 2 each, plus you’ve got significant travel time getting between this widely spaced places. I don’t think this will work, particularly if you try to fit in a spin on the Autobahn. Does your 16 days count your flights from DC? Day 1 is overnight flight, arriving, jet lagged and sleep deprived, on day 2. Day 16 is entirely taken up with your flight home and day 15 may be taken up getting to London or other departure city which only leaves 12 or 13 days “on the ground.”

I would visit the friends and family in London first. You can spend “quality time” with them on day 2 when you’re probably up for conversation, getting acquainted with the neighborhood and minimal sightseeing but probably aren’t physically and emotionally ready to tackle serious on-your-own travel or sightseeing.

The best time to go would be the fall or late spring as things are cheaper and the weather is still nice. I think 16 days would be a little tough unless you’re flying to each destination…..otherwise the travel time is quite long. There is a cheap airline in Europe. ryanair.com

Flying will save time for parts like getting to and from Rome, but for most of these trips (London-Paris, Paris-Amsterdam, Rome-Venice) the train will be faster than flying. Any flight takes 5 hours by the time you add getting to/from the airports, check-in time, security time and actual flight time. A flight in the early afternoon kills the entire for traditional sightseeing.

That is a lot for 16 days. I would say do 3 cities so you can spend more time in each and really get to see the city so by the time you settle in, it is not time to pack up again.