How do you translate "place" in an address into Chinese?
In English, as we all know, there are many ways of saying a "way", like road, avenue, street, boulevard and place of course. They all have different and specific meanings. However, in Chinese, we do not use that many different words. Therefore, what you would basically do is to just translate "place" into "街" or "路" and that is it!

Also, as the rule says, in Chinese, address is written from biggest to smallest, thus as for yours, it would be translated to


  美国，纽约市，古斯塔夫·L·利维街一号，邮编：10029


Though the name of the street can be translated into Chinese by its pronunciation, it is suggested to include the English name of the street in order for people to locate the address easier.

For your curiosity, please refer to this link for Chinese correspondence of many types of "way" in English.