Netherlands Itinerary - 6 days

In my opinion (and it's just an opinion, so take it with a grain of salt), your logic is backwards.

To make the most of six nights in the Netherlands, stay in one place all six nights, and take day trips to the other places you want to see. You will not minimize travel time by relocating, because whatever time you save will be eaten up by packing, checking out, finding the next hotel, and checking in.

Plus distances are small enough in the Netherlands that you will not waste a lot of time on trains. Amsterdam to Delft, for example, is only about an hour each way.

Either Amsterdam or Haarlem would make a good base. But I recommend staying put!

Have a great trip!

Stay in Leiden and day trip to Delft. Add a day to Amsterdam?

Distances are short in this part of the country and on the main lines the trains run at least every 15 minutes.
You can stay in Haarlem, which is 15 mins from Amsterdam and 20 mins from Leiden. Leiden is less than 15 mins from Den Haag (The Hague) and 25 from Delft. (Leiden is also just 20 mins from Schiphol airport.) While there is no real reason to change accommodation, splitting between Haarlem and Leiden makes sense.
You'll probably find 2 days a little bit much for Delft and Leiden. That extra time can be invested in The Hague, if only for the wonderful Mauritshuis museum, and in much overlooked Utrecht (40 mins by half-hourly train from Leiden).
If the weather is fine, a day trip to Dordrecht and the windmills of Kinderdijk would be lovely. (Kinderdijk can be reached from Dordrecht by using the Waterbus river ferry. And for the return journey you can use it to get to Rotterdam. You find their schedule on their website.)
Consider using the TripKey for your public transport. I hear good experiences. Details on their website.

I agree with some of the other posts. Stay in one place and take day trips to other locations. Haarlem is a good choice because it's a smaller town that is well connected and easy to navigate. However, you might want to stay in Amsterdam to enjoy the city's nightlife and many fabulous attractions. As others have recommended, I'd use Tripkey to get around on the buses, trams, and trains. Good luck.

Thank you everyone for your feedback. This is the shortest trip to Europe we've ever taken and it's really hard to commit to an itinerary! We are apparently so indecisive that we are now looking at staying in Belgium for 2 nights after our 2-night stay in Amsterdam. After listening to the Rick Steve's Belgium podcasts during our last road trip, we are excited about enjoying some of the beauty and hospitality that Belgium has to offer, and trying Belgian treats like beer, waffles, fries, and chocolate! Bruges sounds like a 'can't miss' destination for us now. So, we're throwing this whole idea of "minimizing travel time" out the window and just going for it. We will probably spend our last night 2 nights in Haarlem.

If you are not going to the east (Apeldoorn-Deventer-Arnhem-Kröller-Müller Museum and Park), you might as well sleep in Amsterdam. The commuter trains provide excellent daytrips without moving your hotel. I daytripped to Delft, but did not attempt to include The Hague. If you're doing The Hague or Rotterdam (neither of which did you mention ?), I'd consider an overnight or more. (You also didn't mention the two big windmill exhibition parks.)

You make it reasonably clear (?) that your air travel will be in and out of Amsterdam, so I can't endorse moving to Brussels (or even Rotterdam) before going home. But it depends on the departure time of the plane home. I personally prefer Antwerp to Brussels, but that's a matter of taste. Have you gotten some time and cost estimates for the train travel? It often seems like posters here treat Belgium as part of the Netherlands, and it isn't. Again because of commuter train opportunities, Brussels or Antwerp are good for a week, with multiple daytrips.

It sounds like you have traveled enough to know whether getting back to Amsterdam (instead of flying home from BRU, which is easy from the U.S. east coast) will be tedious for you.

First thing's first: TripKey. Don't leave home without it.

Second: unless you're trying to save money, stay in Amsterdam. There's more to do there, and you can walk into Centraal station and snag a train to anywhere in minutes. Delft is a day trip, Leiden is a day trip, Haarlem is a day trip--(do it on Saturday, the market is cool).

Third: For Anne Frank, I hope that you hit that website exactly 2 months to the day of your planned visit, or you might have been out of luck. Yes, it's that nuts.

Sorry for the late reply and if I've already duplicated other folks' responses.