We're less happy when we see people doing better than us. We're less happy when their status signals are more impressive than ours. Thus, visiting Manhattan or checking in on Facebook friends can be depressing.
Insofar as inequality results in the self-perceptions of being less successful than others, inequality can trigger dips in happiness. Note I didn't say "makes people unhappy" - because most Americans are still pretty happy or very happy. They're just somewhat less happy than if they didn't have to see a bunch of people that look great, have cool stuff, and go on amazing vacations.
According to one study, being around the rich makes us want to buy status-enhancing "visible goods", like fancy cars or clothes. And that might reduce household savings by about 3% a year for the non-rich folks. Note I (and the study's authors) said "might", because who knows what people would do if they spent less on visible goods - they might just spend more on non-visible goods.
So is the lesson if you want to be happier, live around people poorer than you? Kinda but it's nuanced: living in affluent neighborhoods increases happiness because these neighborhoods have qualities conducive to happiness (e.g., less crime) but living near poor neighborhoods increases happiness because of those less-than-noble social comparison effects. As the authors of one study put it:
"...individuals in fact are happier when they live among the poor, as long as the poor do not live too close." Firebaugh and Schroeder, p. 805
References:
Bertrand, Marianne and Morse, Adair. Trickle-Down Consumption. NBER Review of Economics December 2016, Vol 98/Issue 5, p.863-879.
Fenne große Deters and Matthias R. Mehl. Does Posting Facebook Status Updates Increase or Decrease Loneliness? An Online Social Networking Experiment; Social Psychological and Personality Science; December 2012, Vol 4/Issue 5, pp. 579 – 586.
Firebaugh, G., & Schroeder, M. B. (2009). Does Your Neighbor’s Income Affect Your Happiness? American Journal of Sociology, 115(3), 805–831.
Kross E, Verduyn P, Demiralp E, Park J, Lee DS, Lin N, et al. (2013) Facebook Use Predicts Declines in Subjective Well-Being in Young Adults. PLoS ONE 8(8): e69841. https://doi.org/10.1371/journal.pone.0069841