Question

What are the places(in order)that I need to find Articuno before finding it in Sea Spirit's Den?

Answer 1

It isn´t specific places you need to check in pokedex when seeing it the first time.You have to encounter them 12 times before sea spirit den.

Source

Hope I helped.

Answer 2

There is no order. Articuno appears at a random route which you can check with your Pokedex every time you enter/exit a route or building.