Travel destinations near Hanover Germany

Charming towns/villages: One of the Half-Timbered-House Routes surrounds Hanover.
https://www.deutsche-fachwerkstrasse.de/en/Routes_Cities/From-the-River-Elbe-to-the-Harz-Mountains.html

Certain towns have some particularly attractive "Weserrenaissance" buildings. Not included on the above route but nearby are some additional places I've been and appreciated in the Hanover area:

Bremen (UNESCO WH town hall)
Hamelin (Hameln)
Rinteln
Bückeburg (palace)
Lüneburg
Hildesheim (UNESCO cathedral)
Hannoversch Münden
Goslar (UNESCO old-town, quite beautiful)

You've made your WW II wishes clear. Still, if you're near Hameln, the location known as "auf dem Bückeberg", where Hitler's "Thanksgiving rallies" once drew throngs of supporters, makes for a nice drive-by, especially if you've ever seen pictures of this event. What's so nice about it? Nothing on that huge slope now but green, all peaceful and serene. Nazis all gone.

I have been looking at this area as well. I might add Celle to Russ's list. It is very close Hannover.

Thank you both! 😁

Münster is a bit farther (about 2 hours by car - slightly longer by public transport) but it's a very interesting medium-sized city with a gorgeous cathedral dating back to the 13th century (and an astronomical clock). St. Lambert's Church also has some interesting history in that you can see 3 cages hanging from the steeples that once held the bodies of tortured Anabaptists back in the 16th century. There are a number of other interesting sights as well.

The Heath might be nice in April

1hr north of Hannover direction Hamburg/Lübeck

Check out this remote spot
Nice Hotel with a good restaurant and a delicious breakfast

https://www.tuetsberg.de/en/

Stay 1 or2 nights there on your way to Lübeck on the Baltic sea
1,5 hr north of Tütsberg
Stay in Travemünde a nice seaside town

https://www.visit-travemuende.com/

and see nearby UNESCO World Heritage site Lübeck

https://www.visit-luebeck.com/

Several good, worth while recommendations here logistically. I would also suggest Minden an der Weser. Take the S-Bahn or the regional train from Hannover...very doable.

If you're interested in trying a beer in this region not too far from Hildesheim , aside from the one in Lüneburg, there is Einbeck, ie its
brewery in the small town of Einbeck .

You have more choices in this regard , all depends on how far you want to go from Hannover. Further west from Hannover towards Osnabrück is the small town of Herford... its brewery, one of the best beers I've had in Germany, "Herforder Pils".

I would say go to the Harz. They will be gearing up for Walpurgisnacht (April 30), and depending on the exact dates you might be able to get in on some of the events. Towns like Braunlage and Benneckenstein and Schierke are normally of little consequence, but cute and great for hiking. Larger towns in that region that are absolutely worth visiting are Thale, Quedlinburg, Goslar, and Wernigerode. You can also compare former East / West towns to see the difference and you can get some great nature, culture, and half-timbered history. Take the narrow gage train to the Brocken, the highest point in northern Germany and home to a weather station that was absolutely for sure never-ever used for Cold War spying. Visit the Hexentanzplatz and enjoy the stunning views from the cliffside eatery. And bask in the witching festival events, a cultural touchstone and tons of fun. And Quedlinburg and Goslar meet your UNESCO wish as well as being charming villages while Wernigerode has a good castle.

Nobody mentioned Marienburg Castle so far.

And if people mention Lübeck I would more mention Schwerin with Schloss Schwerin. The old city with the dome south of center lake Pfaffenteich is beautiful with a lot of small shops and nice restaurants and cafés.