There are some nice pathways along the banks of the river. Some areas are a little secluded from the traffic and there are play areas for kids. Also there are some tiny sandy "beaches" (wouldn't recommend bathing though because it's a river after all). The trip could be combined with crossing the old bridge spanning the river.
It's all just a nice walk, or bicycle ride, with kids or without.
This is one of my favorite places in Elverum. When I lived there, I used to buy a "whole-year-ticket", so I could visit whenever I wanted.
The museum has aprox. 100 000 visitors each year, and is situated on the banks of the Glomma river (the longest river in Norway, around 600 km). A large part of the museum is out-doors, with small cabins (loggers' cabins mostly) brought here from all over the county of Hedmark.
Inside the main building you can learn about all the different activities that take place (or took place) in the forests of Norway. For instance: logging, hunting (with weapons and traps), and fishing among others. You´ll also see different animals and birds (not live ones) that live in the forests.
The outdoor section is partly situated on a small island in the river, Prestøya. Here you can see the old cabins, different old methods of trapping are demonstrated, there's a fishing pond for the children, and from the two bridges you can watch the torrents of the river below.
In August each year (the first or second weekend) a big fair is arranged on the premises of the museum, Nordic Hunting and Fishing Days. This is a fair for hunting, fishing, camping, and outdoor activities in general. The fair lasts from Thursday to Sunday, and is visited by 30 000 people each year... Really recommendable!
The Elverum Music Festival (Festspillene i Elverum) takes place in the first half of August each year, and lasts about 10 days. The concerts are mainly of classical music, often with well-known national and international performers. The concerts are held in churches, on farms and also out-doors in a large distirict around Elverum.
I prefer Forstmann (at the Forest Museum), Steinbua or Peppes Pizza. A very nice new restaurant opened in 2006: "C" (the name of the restaurant), is located in the hotel Central in the middle of town.