What language of the Scandinavian countries
(Sweden, Denmark (and Greenland), Norway, Iceland, maybe Finland)
is more similar to the Old Norse?
Not in writing (I'm pretty sure they used another alphabet), but in pronunciation and similar speech.
Iceland without a doubt. The pronunciation has obviously changed, but the grammar and vocabulary is very similar. Finnish is not even in the same language family. It's about as similar as Mandarin is.
You should try /r/linguistics! I'm sure you'll receive a much better answer.
I know Icelandic is pretty similar. The little grasp on Anglo Saxon i have also shows some bare similarities.
Iceland, Faroe Islands and Norway, in that order. For Norway, western-Norwegian dialects like the Sogndal and connected areas would be closest.
The title of the dictionary I use for my Old Norse class is Old Icelandic, so without knowing modern Scandinavian languages, I would say Icelandic.