Manhattan has always been more slice than pie for me, and I'm years out of date, plus I'm now in New Haven, so I'll largely defer to others.
Your use of "We're close enough" makes me think you aren't IN Manhattan. True? If so where are coming in from?
Also "pie" makes me think you're looking for sit-down experience, which rules out a lot of places. Yes?
If it's from north of Manhattan, I'll suggest a visit to Patsy's in East Harlem. The bonus is that you can do a mini test run by getting slices from the small, adjacent space with its own coal oven and see if you like it. You can double park on 1st Ave, and get 3 slices for less than the Triborough Bridge toll, then cross over the free bridge to the Bronx and get on either the Bruckner or Major Deegan. If you like it, then there's a dining room next door for next time.
John's and Lombardi's both always left me thinking, "I like New Haven more," which isn't a huge knock, just what's so.