I'd say he is closest to Captain America but is also friends with Tony Stark; the difference is that Stark has probably annoyed/hurt Thor more with his less than favorable (but realistic) actions over the past few years while Cap has been largely a hero in the Asgardian mould (valiant, morally upright, strikes awesome poses). The dwarves and other craftsmen would understand and like Stark more, one would think.
an honorable mention would be Spider-Man; the most human and neurotic superhero can banter it out with the best.
Beta Ray Bill counts as an Asgardian I suppose, so his godly best friend is most likely Hercules- who else would Thor let play pranks on him (sans Loki) and laugh it off?
People forget that Thor and Iron Man once shared the secret of their secret identities only with each other, amongst all the Avengers. Not even Cap was trusted enough and during the 1st armor war, Thor was still reluctant to take sides with Cap, even though Tony was in the wrong in the way he went about things.
I thing this all changed when Cap proved worthy to lift up Mjolnir. Thor felt more of a bond with him from then on and Iron Man actions during and post Civil War probably reenforced this