Within 5 min you can reach the titular forest (old German "Holz"), 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 mountains within approximately 1 hour by car.
About 10 minutes drive away in Hildesheim, a 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 summer.
Within 40min 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/).