Addvar can be found during the day behind the stall in the market. At night he is in Addvar's House in Solitude.
When you first enter Solitude though, he will be near the gate witnessing Roggvir's Execution
Addvar is a merchant, and operates a stall which sells mostly food, but some ingredients
Items for Sale
Addvar sells the following items:
You can ask Addvar about where he gets his fish (down at the docks, if you can avoid the East Empire Company workers)