Q. What is it supposed to be on the show?

A. A casual restaurant.

 
Q. Where is it supposed to be on the show?

A.  In New York's Theater District.

Q. When did we see it on the show?

A. In Episode 8 of Season One of Resurrection.
 
Harrison wants to meet with Dexter to talk, but Dexter has been planning to wait outside the theater showing Hamilton, for Al (“Rapunzel”) Walker to come out after the performance, when he plans to kill him.


But Dexter is finally beginning to establish a decent relationship with his son, so he can't afford to not be there when he needs him.

He compromises by agreeing to meet Harrison in a restaurant in the Theater District, which is close to where he plans to abduct Al.

Once there, Harrison tells Dexter that he is feeling guilty about not being able to help Elsa, who is on the verge of being homeless because her lousy landlord, Vinny,  refuses to fix the serious problems in her apartment.

Dexter suggests that perhaps he can talk some sense into Vinny, saying he can be “persuasive”.  This worries Harrison at first, and he quickly starts to say that he doesn't want Dexter to kill him. But Dexter assures him that despite being a jerk, Vinny doesn't meet Harry's code.

Harrison's appetite returns and Dexter, in a hurry to get to Al, calls for the check. 

A. This is basically what it seems to be in the episode: an Applebee's restaurant in New York's Theater District.
 
The address is 234 W. 42nd St, in Times Square. (The Theater District is a somewhat larger neighborhood which includes the smaller Times Square area.)

The restaurant is located on the south side of 42nd Street, between the Hilton Times Square on it's right and a Dave & Buster's on it's left.

Given the gaudy, bright lights of Times Square, this particular Applebee's appears to be larger and glitzier than most. It is two-levels, with a spiral staircase leading upstairs. and it certainly looks like they shot the scene inside the actual restaurant.

Dexter has Harrison meet him there because Dexter is stalking Al (“Rapunzel”) Walker, and Al is currently attending a performance of the Broadway hit Hamilton.  So as you might expect, this restaurant is just a very short walk from the theater where Hamilton is playing.
 
 
Here is a matching StreetView of the restaurant: 
 


Here is an aerial photo of the location.  And here is a map link.