Engagement photoshoot next week - recommendations on this plan?

My partner and I are planning a 3-4 hour engagement photoshoot in New York early next week with the following plan. We live in LA but we're traveling in New York. For me, it's kind of a nostalgia photo session after having lived in the city for over 10 years. For him, it's his first time and he only knows the city through mainstream Hollywood (think Avengers, John Wick). The vibe is candid natural photos following us around on a date as we explore the city.

A couple of questions:

• Is this doable in 3 hours? We'll basically be speed running, but 4 hours is at the top of our budget ($1450). I've never booked a photographer before, so I don't know what kind of pace to expect. For 3 hours, what would you skip off this list? We're tentatively doing 1pm to 5pm (4hrs).

• What's the best way to manage shoes & outfits that look nice enough for an engagement shoot in mid February? Pack cute white heels in a bag, but run around in boots/coat? Our outerwear is not the cutest. And I unfortunately haven't picked an outfit yet, and I think it will be a knee length dress + tights.

• Any other specific spots along this route you'd recommend? I'd love a few indoor casual spots, but the only cafe I picked is devocion.

route: 

• brooklyn brownstones, in the street, brooklyn heights

• dumbo: park with view of bk bridge, street shot between buildings with view of mh bridge

• cafe shots, at devocion at york street

  • a shot looking outside in to us thru cafe window

• continue walking to f train, cute subway shots, platform, interior of car

• exit at bryant park

• ny public library, indoor and outdoor

• Grand Central

  • corner of 42nd and Vanderbilt
  • avengers shot down park ave (i know it's on the car overpass...)

• taxi, entering, interior, exiting, head uptown

• Central Park, fountain? met? i'm very open to suggestions here

• holding blue Greek coffee cup (I'm trying to tell him I never see them anywhere... he doesn't believe me haha) 

• buying at hotdog from the cart (maybe in front of the met?)

Thanks!