Is it possible to squeeze in Berlin, Frankfurt, and Amsterdam into a 7-10 day trip?

You definitely should not try to do all three if you only have seven days. If you only have seven days then pick one city to pair with Frankfurt.

If you have ten days that could be doable but would still be rushed. You can easily travel by train between all three cities, but doing so takes the better part of a whole day. So a lot of your already short trip will be spent moving from one city to another.

Honestly, to see even half of what Berlin has to offer could take your whole ten days and then some.
There is plenty to do in both Amsterdam and Berlin for 20 somethings. Ask them to do some googling to find things they enjoy in both cities. Rick Steves also publishes guidebooks just for Amsterdam and just for Berlin which they could peruse.

If you want to see castles then you might want to spend more time in the Frankfurt area where you could easily do a day cruise down the Rhine, where you will see plenty of castles. A google search will tell you what there is to see along the river and where to go to pick up a cruise.

Also, you'll save yourself some time, whether you see two cities or three, if you book "open jaw" flights, that is, arrive in one city and depart from the other, so you don't have to backtrack to the city where you arrived. You can check prices for open jaw flights if you go to Google Flights, choose "multi city" instead of "round trip" from the drop down menu and put in your potential arrival and departure cities.

If you've never been to Europe, then know that getting around between big cities and within cities is usually easy via public transportation. However, getting the hang of it can eat up a LOT of time, especially if you're not experienced with it, so "ten days in Europe" is actually not a lot of time when you factor in that your arrival day is not a full day, your likely jet lag, your days traveling between cities, and figuring out how a transit system works when you set out to go sightseeing.

If you can eliminate one city from your trip, you will have more time to slow down and enjoy the two you do visit.

Kayla, thank you so much for your great words of wisdom. It sure can get overwhelming planning a trip to somewhere you've never been. On the maps it doesn't look so hard, but I definitely appreciate that in real life nobody wants to waste so much time on transportation. Most likely we'll end up 9 or 10 days, since 2 will be spend in Amsterdam. I will definitely look into that river cruise.

Have you looked at guidebooks for the 3 cities or at the information on this website in the "Watch,, Read, Listen" section? Do this and make a list of the sights you both want to see in each of the cities and then decide how much time to spend in each city. People on this website talk about how much there is to see and do in Berlin, but I only spent one full day there and have never had any interest in returning. Different people have different interests and priorities, so you need to plan according to your own interests.

If you have 10 days it is extremely narrow but possible if you fly into Berlin and out of Amsterdam.

Route would be Berlin (3-4 nights) - train to Frankfurt - Upper Mid Rhine Valley (ship ride 1 day) - train to Amsterdam (2-3 nights).

Not meaningful with less than 9 nights.

Sure, just plan on flying between them. Local flights are no more expensive than driving (gas is @ $7/gal) or the train for the distances you're talking about. Plus driving or taking the train is an entire day lost each way in travel.

August is prime winefest time. That will probably be of more interest than bouncing around cities. Just stay in Mainz and see the Rhine, the Wine Road, the Mosel, and everything in one really nice part of Germany. And you can do all that on one $50 train ticket.

I'm going to disagree with the idea of flying between cities. Both trips Berlin to Franfurt and Frankfurt to Amsterdam can be done by train, without changes, in just over 4 hours. That's city center to city center.

With flying you have to travel to the airport, get there two hours ahead of time, take the flight, and travel to the city from the airport.

Travel time for both would be about the same. However, with train travel you don't have to go through security and it's a lot more comfortable. And you get some nice scenery. If you took a morning train, you could get into the next city around lunchtime, drop your luggage at your hotel, and have the rest of the day to sightsee.

I also agree with flying "Open jaw." This will save you a lot of time.

OP just need to fly-in Berlin and put things into right order through to Amsterdam - that's it.

...head to Amsterdam for a couple days...

We also want to spend a few days in Frankfurt because my nephew (20
years old) is stationed in the Air Force, based in Spangdalehm and
want to be close enough for him to come stay with us and visit with
us. Some of our must-do's are to visit a few castles during our trip.

You can do this trip comfortably by train with 9 nights in Europe by flying into and out of AMS; do the basic travel legs in the late afternoon/evening to allow for more daytime sightseeing. Here's an example with sample rail journey times from DB...

(Frankfurt is a less-desirable location for proximity to Spangdahlem. I'd go with COLOGNE instead, which is also closer to Amsterdam.)

1.) Amsterdam: Days 1,2 + half a day on Day 3 + train to Berlin (around 6 hours, like on the direct IC train...15:33 - 21:51)

2.) Berlin: Night 3 + Days 4-6 + half a day on Day 7 + train to COLOGNE (around 4 hours, like on the direct ICE train... 14:56 - 19:15)

3.) Cologne + Upper Middle Rhine Valley: Night 7 in Cologne with Day 8 train outing to the Upper Middle Rhine Valley for cruise and tour of Marksburg Castle in Braubach (can Nephew join you for this outing?) Then back to Cologne for Night 8.

Then Day 9 in Cologne (visit w/ Nephew?) + train to Schiphol Airport for last night (around 3 hours, like on the ICE + IC train sequence, 17:41 - 20:41. Fly out Day 10.)

That was basically my idea posted above but without flying in / out of the same airport. Travelling the route twice is more or less waste of time. This way they can also include Frankfurt to see the nephew.

To use one night the best way OP can take a night train between Berlin and Amsterdam - of course not everybody's way of travel.

I would also disagree with flying in between cities. Schiphol can take a long time to get through, both in terms of walking to your gate and getting through security. The airport in Berlin is way outside the city and even by taxi (quickest, but most expensive way) from anywhere in the city takes 25-30 minutes. And BERs security lines can be long and slow moving as well. I have only been through the Frankfurt airport once but remember it also being very big with lots of walking involved. You would not save much, if any time, but you would definitely increase the hassle factor. And as stated above, you'll be able to see the countryside on the train.

Amsterdam to Berlin is a local flight. There's no need to get there more than 30 minutes early, you don't go thru Customs. It takes 1 hour and 20 minutes. It costs 76 Euro. No train is going to match that.

Berlin to Frankfurt is is also local. It's an hour and 10 minutes. Cost is 90 euro. This is how you should move around.

Fly into Amsterdam, out of Frankfurt. This should be easy from anywhere in the US.

I would cancel Amsterdam.

If you get to Amsterdam or Frankfurt airport thirty minutes before the flight you will miss your flights.

Security alone, if busy, can take more than 30 minutes. And then you have to walk to the gate.

In many cases, boarding closes 10-15 minutes before the flight.

Sorry, but that's bad advice.

You could do all three cities in three days. But would you want to? So then it is up to you how long you want and do you want to? The transport between the three cities is the same no matter if the visit is one night or 30 nights.
You both want to see Berlin. Bingo. First city. Then Amsterdam at most likely, you say, at the end. That leaves the itinerary as Berlin, Frankfurt, Amsterdam.
No way are you going to see all you want in any of the cities. So accepting that if you can, the itinerary is one of convenience.

Even if you have ten days, I'd suggest not more than two cities. Your arrival day may be "lost" due to time of arrival, jet lag, and getting to initial hotel. Your departure day is also a day that doesn't count. And when you relocate you'll usually lose at least one half to three quarters of a day.

It appears that Frankfurt is a must in order to visit with the nephew. If so, ther the other cities should be ranked in importance to both of you. Then select one.

All three cities can be done in ten days, but it will be very rushed. You'll want good memories. Not just memories of getting from one place to another.

Just offering food for thought.

I don't know if you're meeting up in Spangdahlem-- if so, Koblenz is nice and close. So is Trier albeit in the opposite direction (but not far.) I spent a few months in at Ramstein eons ago and we enjoyed the castles on the Rhine during off days.

To disagree with the crowd, I see no problem seeing all three cities. Heck, when I was in Ramstein we drove to Amsterdam and back in one weekend. I wouldn't do that now that I am older (but no wiser). But at 28, sure!

In any case, have a great time!

Sorry Frank, but I routinely get to Frankfurt 30 minutes prior to the boarding time (for flights within the EU) and have yet to miss a flight. Going two hours early is ridiculous.

I routinely get to Frankfurt 30 minutes prior to the boarding time

The important word here is routinely. You are familiar with the airport, know where to go, how things work, you speak German etc. For someone that is not as familiar with the airport, 30 minutes is more risky.