"I am going to that bank, there at the castle."
Translation:Abba a bankba megyek, ott a várnál.
It's not clear from the English cue whether the speaker is going into the bank, or merely going toward it; perhaps "ahhoz a bankhoz" should also be accepted?
into is used infrequently. The only purpose of "into" is to express penetration of a closed in area like a mouse goes into its hole