Within 5 min walking distance you can reach the titular forest (Diekholzen is an old German word for "surrounded by forrest"), where you can wander on many different trails with roundtrip options. If you like to have a specific destination, you can walk to the lookout tower (it has a small restaurant too, take a look at the opening hours - probably just on weekends) or Haus Escherde.
You can reach the Harz mountain range within approximately 1 hour by car.
About 10 minutes drive away in Hildesheim, an old diocesan city of 100,000, there are many more shops and two malls. Hildesheim is more than 1200 years old and has a few unesco world heritage like St Michaelis church and the cathedral with its 1000 year old rose bush. The Jo-Beach resort is a small lakeside beach with a bar and restaurant, which is a nice option for cooling down in the summer.
Within 45min you can reach Hanover, the capital of lower Saxony. In Hanover is a renowned zoo and many more (cultural) activities to experience (find out about them in our treasure chest full of pamphlets).
There are a few small amusement parks in the region: Rasti-Land 30min (https://www.rasti-land.de/), Family Park Sottrum for smaller children about 25min (http://www.familienparksottrum.de/).
If you like to go to a large amusement park you can go to the Heidepark Soltau about a 90 minute drive (https://www.heide-park.de/).