Is Richer Nicer?

This post is long overdue, I meant to write it at least three weeks ago, but I find myself just now taking the time to create it.
In class, we spoke about neighborhoods, specifically train stations within a town. We watched people state observations about the Kenilworth Train Station to determine what could be considered a mark of it being a train station in a high class neighborhood.  Things like a nice waiting room, potted plants, and a roof over the bike racks demonstrated that Kenilworth is wealthy. We then proceeded to watch a video Mr. Bolos had filmed of the Union Pacific/West Line. We took notes on many things trying to find similarities and differences to the town of Kenilworth and its train station.
Some of the observations included lack of nature, home size (bigger or smaller), how industrialized the area was (if there was a factory), and even little things like the decorativeness of street lights. It's incredible what those little details bring. And when we had our class discussion after watching the film, the word "nicer" was used a lot.
Mr. O'Connor kept correcting people by saying, "you mean 'higher income,' right?" Everybody would backtrack and say yes, I meant higher income. But my question is, is it so wrong to make the two adjectives interchangeable?
When I think of a "nice" neighborhood, it can always be described as "rich" or "wealthy" as well. "Nice" neighborhoods, in my opinion, have good schools, up-to-date and taken care of buildings, security, green space, good-looking homes, etc. All of those things require money as well, so then, aren't "nice" and "wealthy" almost synonymous in that case?