I assumed you realized we were constraining ourselves to places with a High or Very High HDI.
If nobody has any money at all, would you not say inequality is low? If everyone in Tajikistan has $5 except the president, Emomali Rahmon, is inequality not low?
I suspect you are looking for a pairing of HDI and Gini, which factors in both the development (and hence the standard of living) and the inequality.
Sweden: (Gini: 0.25, HDI: 0.933), France: (Gini: 0.31, HDI: 0.901), Canada: (Gini: 0.33, HDI: 0.926), USA: (Gini: 0.48, HDI: 0.924), South Africa: (Gini: 0.65, HDI: 0.709).
Now, Tajikistan has an HDI of 0.66 ("medium"), and Azerbaijan 0.756 ("high").
Kazakhstan might surprise you, the HDI is 0.817 ("very high"). The standard of living there is actually good, in spite of what you may have seen on Borat - incidentally filmed in Romania. Almaty's been on my list of places to visit for a long time :) [1]
[1] https://en.wikipedia.org/wiki/Almaty