The first date usually takes place at a lounge. If you’re located in Brooklyn, the Brooklyn Marriott is a very popular option.
As you enter, make sure to ask her if she recognizes anyone and if this makes her uncomfortable. (This is especially important at a place like the Brooklyn Marriot, which is a very popular place for dates.) Just in case, always have a backup plan. Also, some girls are uncomfortable taking the escalator/elevator, while some would rather not have to climb up the stairs. So check her feelings on it before ascending.
On the second date, some people go to a different lounge, while some want to do something slightly more scenic. A walk along the water or in a park always creates a calmer atmosphere. (Keep in mind that in some places, יחוד may be an issue. Problems of פריצות should also be taken into account.) In the winter, a place like the Winter Gardens (on the southern tip of Manhattan) is a good idea. [There is a lobby with palm trees in it. If you go up the stairs, there is a hallway which leads to a string of buildings, each one with a beautiful lobby.] It is always a good idea to check out the place beforehand to ensure that you don’t get lost. This is especially important if you plan on going to Winter Gardens.
The next date can take place over dessert in a restaurant, and you may choose to do a full meal on a later date. (Some individuals are מקפיד not to date in restaurants.) Other popular places are the Staten Island ferry (or some other boat ride), bowling, the Empire State Building, arcades, mini-golf, or a pottery place.
Here I would like to off on a tangent. The purpose of dating is for the boy and girl to get to know each other, in order to figure out if it’s a good match, not to socialize. Socializing is necessary to accomplish this task, but it should be used as a means and not as an end to itself. For example, a trip to the zoo or museum is probably more conducive to talking about the exhibits. This will not give you much insight as to who the girl is. The same is true for any place where you are engaged in an activity. A girl may be more interested in what is happening, and if you push away her comments she will probably interpret that to mean that you don’t care about her feelings. She may also want to test to see if you can socialize without focusing on a goal. I therefore suggest avoiding these places for the first three or so dates, when there is still plenty to discuss. (A scenic place which won’t lead to distraction is best.) More engaging places can serve to lighten the atmosphere during the heavier השקפהdiscussions which will take place later on. They can also fill time when you run out of things to discuss.