Commonly known as Coral Bells.

Seen at Battery Park in New York during my visit in June,17.

This year it seems gardeners all over NYC were planting one or more of these varieties
and there are hundreds of them….
you must have the nursery label to know exactly which one…
however :
seems its some hybrid variety of Heuchera americana  var: ????/  what series of hybrid ???
cant tell if the flowers are white or faded.
It seems to me that the stem of the flower is not too delicate,  so may be the Dolce series.  ….

There was no label visible.
Thanks for the info.

Look at these sites and you will appreciate the difficulty in id from a few pictures
and to appreciate how wide and deep is the hybridization industry please read this
and you will appreciate that insisting on naming a plant from  4 pictures such cases is not a choice.
one variety that was also popular is this:
and there is one picture in the wiki page, worth a lot of words

There is a list of all plants growing at Battery Park.
Your plant could be:
Heuchera ‘Plum pudding’, 
H. micrantha var. diversifolia ‘Purple Palace’, 
H. ‘Cherries Jubilee’, or
H. ‘Pewter Veil’.
You can most likely rule out ‘Silver Scrolls’, ‘Snow Angel’ and ‘Whitecloud’ as they are the wrong color.

Thanks for the list of plants …

I will try to match my plant from your given options.

Carmelita is right possibilities are many, but you cant match colors of one day.
if you read the refs you will see leaf color changes as season goes on light, age of plant etc
Nice to see you …
agree with you that possibilities are endless