Considering this person is grieving, I didn't bring up on the list that simply put, there's no guarantee this person went to Valhalla. There wasn't even any connotation that the loved one lost had ever served in a warrior-type capacity, let alone was battle-slain. Within our tradition there are a number of Halls and Gods that play host to the dead.
Hel - simply put is the place of the dead. Etymologically it's believed this roots to simply the word for grave. As the place where the dead reside. It has no connotations of good or evil in and of itself.
But within hel there are 2 places known for where those who committed evil in life (oathbreakers, murders, etc.) were known to go:
- Nifolhel - where those who have committed evil go
- Nastrond/possibly also Wyrmsele (in OE)- where the most evil are sent
Battle-slain - if not evil, go to Valhalla or Sessrumnir.
Vingolf (according to Snorri some of Odin's dead go here instead of Valhalla, but it may refer to a hall hosted by the Goddesses instead... this one is unclear).
Those who die at sea - go to Ran
Geofon (aka Gefion/Gefjon) - I think this Goddess is also said to take some of the dead. But can't remember for certain.
And that's only the places and/or Gods/Goddesses I remember off the top of my head. I seem to think there are more halls that are said to play host to the dead.