Near Hannover

I would include Hamburg and / or Lübeck as additional impression.
Schwerin is a beautiful town but little bit too far away for you?
Goslar / Harz I would plan more time.
Not sure about including Hildesheim and Wolfenbüttel but it all this is a question of personal taste.

Maybe you also want to visit Marienburg Castle?

If you are going to be in Hannover, I suggest you visit the Harz, there's lots to see there. In 2008, I spent 5 nights in the Harz, based here in Braunlage, and I really enjoyed it.

One day I took the bus to Bad Harzburg, then the train to Wernigerode and toured the castle there. This was the first time I had ever ventured into the former East Germany, and as a child of the Cold War, it was an eerie feeling. I have read that, during the Cold War, East Germany pumped a lot of money into Wernigerode to make it appear prosperous so they could take visitors there to show them how great life in East Germany was.

Another day I bused to Schierke, also formerly in East Germany, from where I took the steam powered, narrow gauge train to the top of Northern Germany's highest mountain, the Brocken. The Brocken, supposedly, was the inspiration for Goethe's Walpurgisnacht in Faust, where the witches danced with the devil on the mountain top.

On another day, I used the excellent bus system to visit neighboring towns, including Clausthal-Zellerfeld. .

Do have a car? if yes do like nature walks?

If so why not stay in the Lüneburg heath area for a night or two?
https://www.lueneburger-heide.de/en

Main season is in autumn when the heath is blooming. So in spring time the area will not so crowed but not less attractive.
We stayed there in a holiday home for a week some years ago and spent a night in two hotels on our way to and from the Baltic sea this year in April.

Here the links to the Hotels in
a)Oberhaverbeck near Bispingen
https://www.haverbeckhof.de/en/

and b) a remote spot near Bispingen
https://www.tuetsberg.de/en/

When you decide to go there definitely do a carriage ride to Wilsede in the center of the nature reserve
https://www.lueneburger-heide.de/service/sehenswuerdigkeit/7506/wilsede.html

When plan to go and need more info let me know

Enjoy your trip to Germany

Check the price of a nonstop to AMS, then continue to Hanover on the train. Just a quick look on matrix.itasoftware shows $675 for the nonstop, but $1350 for the continuation to Hanover, a savings of 50%. Right now there is a direct IC train from Amsterdam Centraal to Hanover around 5 PM.

Thanks for all the suggestions. I wanted to open my mind to new thoughts about the area.

We are planning to go in April. The weather can be an issue. We like to do our sightseeing on foot, usually in moderate sized towns.

We will not have a car. We visited Goslar a couple times by car but that was in the 1970's and 1980's. We spent a brief time in the Harz Mountains and the Heide on those trips. I believe I am too old to rent a car in Germany now and think it would be unwise in any case.

We are considering stopping in Amsterdam for a couple days and then taking a train to Hannover. It is a 4 hour IC train ride to Hannover and then another half hour or so to Celle. It does take time.

We have also considered a couple days in Bremen. We were stationed in Bremerhaven in the 1980's. Our first child (daughter) was born there. I will also think about Lübeck as we have never been there.

Thanks again for the ideas.

If you are there at the end of April for Walpurgisnacht, DEFINITELY do that in the Harz. We did Braunlage and Schierke last year. And hiking in the Harz, seeing Wernigerode, etc. is amazing.

I would absolutely put Hamburg on your list, but I also adore Bremen. Lüneburg and the Lüneburger Heide (heath) are also great options, as is the Altes Land (towns like Jork) if you are coming further north. And yes, Lübeck.

When you decide to go to Lübeck from Hannover its a 2,5 train ride with 1 change in Hamburg to get there.
So maybe Hamburg is an option too

Lübeck and its seaside resort Travemünde is a great spot to visit.
We were there in April this year and did walk on the beach at Travemünde , a short boattrip on the Trave (charmante Stunde)
https://www.youtube.com/watch?v=wpJhzDwIezk
and you can visit the historic towns both
Travemünde https://www.travemuende-tourismus.de/
and
Lübeck https://www.luebeck-tourismus.de/

You can also go from Lübeck to Travemünde and back by boat from 1.April (sommerfahrplan)
https://hanse-travemuende.de/fahrplan/sommerfahrplan-ab-01-april-2023

Thanks again for the suggestions. Gary

I would suggest adding to the list of possible choices another places not too far from Hannover : the town of Minden an der Weser. Lünebirg is one of my all favourite towns in Germany, a bit far from Hannover but staying two nights is what I would suggest. I've been to Minden a few times, the half-timber hoses are a feature there too.

If you do pick Lüneburg or Minden, both cities have the Prussian museums, though different in the particular focus. If you are well into that, they are both worthy of your time spent on their extensive exhibitions.

I haven't been to Celle except at the train station to change trains. If you choose it, I suggest seeing the Bormann Museum in the Schloss, where it presents Hannoverian history. Both Celle and Lüneburg survived the war intact, weren't plastered by Allied bombs or artillery fire, both quickly occupied by the British in 1945.

I didn't mention them before, because they're so far from Hannover. But if you're considering Lübeck (which is a lovely visit), you could also consider Münster or Kassel. Kassel is especially good for Contemporary/20th Century art, but also has a great old-art collection in the UNESCO WHS estate at the end of one of their S-Bahn lines. Besides "very old" Germany connections, Munster is noted for outdoor modern sculpture.

Thanks again for the input. If we decide to stay in the general area, we think the itinerary will be:

Celle 2 nights
Lübeck 2 nights
Lüneburg 2 nights
Goslar 4 nights with a couple day trips in the Harz
HAJ Airport Hotel

Train trips will not be too long.

We are also looking at open jaw options but that would probably limit us to 4-6 nights in the area.

Coming back to this now that I have more time. I have a number of thoughts.
1) Why Hannover? If you are visiting Amsterdam first, it's probably where you are flying into/out of, and as it is a major hub, that makes sense and likely makes it cheaper. So then you can train to anywhere. You don't need a true base if you are staying a few nights in each. So why stick to Hannover?

2) If you do prefer a base or there are flight reasons for choosing one city, consider Hamburg. It is likely easier to get in and out of. Bremen is pretty easy, too--and VERY pretty and interesting. I like it better than Hannover. Bremen is WELL worth a visit regardless, and it has a very different feel from the half-timbered stuff you are worried about seeing too much of. I would consider dropping either Wolfenbüttel or Hildesheim in favour of Bremen.

With that in mind, here are a few thoughts of places in northern Germany that may or may not fit your style of travel. I have written enough about Hamburg itself, so I will leave it off for now.

--Note that in the north, "half-timbered" is almost always brick, sometimes very beautifully done, and the timbering more square. You might also see a lot more reed roofed buildings. You would see this in places like Lüneburg and particularly in the smaller villages. In places like Goslar and even to some extent in Celle, you would see more of the plaster style with slate roofing. In fact, there are all kinds of architectural and regional variations within the category of "half-timbered" that could be a fun exploratory sub-theme of the trip. Lüneburg would also give you the Hanseatic style brick waterfront houses.

Verden is a surprisingly wonderful and undiscovered town near Bremen. It is a horse town, home of the German Horse museum--and even if you aren't a horse person, it could be neat. The horse has shaped human history around the world, and the Germans have been a major horse breeding country for hundreds of years. You may or may not know that about 30% of ALL the Olympic horses in the last 30 years are German bred, for example (as far back as I could find stats). The museum is also partially interactive, with riding and carriage driving simulators and more. The town has a lovely brick-and-half-timbered old town, a local museum, church, and of course farms and hiking trails to explore. Worth a day trip for most people, especially from Bremen, but probably not worth spending a night. But worth mentioning all the same.

If you like nature and being very rural (I know, you mentioned mid-sized cities), then one of the prettiest places I think I have ever seen is the Niedersächsische Elbtalaue. We had to pick up a vehicle in a "town" called Trebel once, and driving there was absolutely stunning. And took forever because, well, there is NOTHING but pretty nature. I don't know, though, if this is something for you without a car. It is pretty hard to get to / around. But better to mention it than not, and you might find a neat little farmhouse to stay in or something.

If you are venturing further north to Lübeck, the flavour of your trip changes as well. I like the suggestion. The Hanseatic element means you aren't just looking at half-timbered houses. Good call to add it.

If you are going to the Harz, you might consider Wernigerode. But the suggestion of Braunlage and Schierke was a good one. I have family with a vacation apartment in Braunlage, and they are there a lot--for hiking, but also because the town is adorable. Same with Schierke. Comparing the two is also interesting because they were on opposite sides of the former border. The Brocken, the highest mountain in northern Germany had a "weather station" on it that was absolutely for sure not anything else and definitely not at all used for spy work in the GDR times. And the narrow gage train is the best way to get up there!

Thanks again HowlinMad for your reply.

We are not actually visiting Hannover just using the airport. When I looked at this area, I was mainly interested in Lüneburg, Celle and Goslar. The Hannover airport was well located, only 30 minutes from Celle by train. The airport is served by Delta Airlines, our regular airline as Salt Lake City (our home) is a hub.

I am not fond of long train rides at the end of long flights so I wanted an airport near our destination. We looked at Amsterdam and Frankfurt to visit the area. After a short stay in Amsterdam, we could have stopped at Münster on the way to Celle. Coming from Frankfurt, we could have went to Marburg for a visit and then perhaps a night in Göttingen before a train ride to Goslar. Still, flying into Hannover and focusing on this area seemed a better option.

I looked at flights into the Hamburg Airport but saw no advantage over Hannover.

We will check flights in couple months to see if the picture changes.