26:00: Adam is at a sidewalk cafe (after their first time having sex), when he phones Emma.
Just then, coincidentally, she pulls up in a car, with another guy, a doctor from her hospital.

         

This sidewalk cafe scene was shot at Toast bakery cafe, at 8221 W 3rd St, in West Los Angeles.

The cafe does have a celebrity following of its own, and was seen on "The Hills".

(Here is a Google StreetView panorama of the restaurant.)

28:17: After their first sexual encounter, Adam brings Emma a balloon to the hospital where she works.
(This location appears several times in the movie.)

That hospital exterior is the UCLA Medical Center, on the UCLA campus in Westwood Village.

To be more specific, the camera is looking west at the driveway/entrance off Tiverton Avenue (north of Le Conte Ave),
outside the UCLA Center for Health Science, the School of Dentistry, and the Marion Davies Child Care buildings.

The scene below was shot just west of that entrance/driveway, in the quad behind the Child Care Center.

37:00: Next, we see both of them at a seaside park, but not together.

We see people playing frisbee, barbecuing, etc.  Adam sees her talking to another guy,
(the doctor again) gets jealous and text's her that "He has really small hands".

 Later, he has a somewhat hostile conversation in the parking lot with the doctor,
who tells Adam that Emma's only using Adam for sex, and will never marry him.

This is Burton Chase Park, at 13650 Mindanao Way, in Marina Del Rey, CA.
A unique spot, it's the only public park in L.A. surrounded on three sides by water & boats.

(The park was also the location of Dexter's wedding to Rita, in the 4th season of "Dexter".)

(Here's Google StreetView for of the park.)

48:54: We next see Emma's friend arrive at a hotel with her fiancé, for a Christmas party.
Her fiancé opens the car door for her, and she's very impressed.

This scene was shot at the W Hotel, at 930 Hilgard Avenue, in Westwood.
It's just southeast of the UCLA campus.  (In the shot above, the camera is looking east.)

Their website can be found here.

(Here is a Google StreetView of the hotel.)

1:01:27: Adam & Emma join his father & his young date (Adam's ex girlfriend) for dinner at a nice restaurant.

They are dumbfounded when the May/September couple discuss having a baby.
Emma eventually can't stand it any more, and walks out. ("Great Scott!")

This scene was shot at STK (another restaurant with a celebrity following),
located at 755 N. La Cienega Blvd, in West L.A.

[Thanks to Mike of MovieShotsLA for this one.]

(Here's a Google StreetView - of the restaurant.)

1:03:54: Adam asks Emma out on their very first official date - for Valentine's Day.

At the time, they are strolling outdoors, at night, in what looks like an urban
pedestrian area, such as the Third Street Promenade - but it's not.

This scene was actually shot in front of the new
Department of Transportation (Cal-Trans) building, at 100 Main Street, in downtown L.A.

That's on the east side of Main Street, at the SE corner of Main & 1st St, near City Hall.

(Here's a matching Google StreetView of the building.)