This line from Monk: Mr. Monk Makes a Friend (2007) motivates this question. Adrian Monk says this just outside his home to a friend of his.
Come on, I live right upstairs.
Just from this, I couldn't tell if he lived on the first floor or just near the ground floor.
"Right next door" implies adjacency, sometimes immediate but, broadly, allowing some footwork:
Next door (broadly): in or at an adjacent place
"Right across the street" is quite ambiguous:
You can also use ["right across the street"] to talk about somewhere that's very close by, but not literally right across the street.¹
However, I find "right upstairs" less ambiguous. Floors being countable, when someone says "I live right upstairs," does it mean they live on the floor directly above the current? Otherwise, they would say "I live [number] floors above," right?