Also relevant here is Italy, where there’s been a much steeper decline in positive test rates in Lombardy, the worst-affected region, than in the rest of the country. Both peaked during the week of 3/24 but Lombardy has fallen notably faster: https://twitter.com/NateSilver538/status/1252689853218803714

Positive test rate by week in Lombardy, Italy

Week ended 3/24: 47.9%
3/31: 33.0%
4/7: 20.4%
4/14: 16.2%
4/21: 10.6%

Positive test rate by week in rest of Italy

Week ended 3/24: 17.5%
3/31: 16.0%
4/7: 14.0%
4/14: 11.8%
4/21: 9.9%

Keep in mind the context here. Do NYC and Lombardy possibly have meaningful levels of herd immunity? Possibly (enough that it may show up in the data) but exactly how much is hard to say (probably far from complete). Think about how bad things had to be to get there, though.