As a part of the companions quests you will need to complete small side missions along the way to increase your reputation. I went to Aela the Huntress for work and she gave me “Animal Extermination”. You can only do one of these at a time. You will need to go to Steepfall Burrow which is west of Solitude and north-east of Morthal:
All you have to do inside is kill a Frost Troll, at least that is what I had to do. I presume that the type “best” depends on your level. If you are struggling with killing it be sure to walk in and out of it’s range to avoid getting hit during the times when you can’t hit it.
I decided to jump down into the small lake to explore a little. It is a complete waste of time as you have to kill 3 snow wolfs and then get to an exit to Skyrim. There isn’t even a chest with some loot!