If you don’t have time to trek down to Katz’s, Sarge’s Deli on 3rd Ave is an option. They have good pastrami, but I get the blintzes. Good chopped liver, too.
Breakfast near Times Square tends to be touristy.
The Red Flame is a typical coffee shop- 44th W and 6th Ave- for a breakfast near Times Square and not far from Grand Central. Expensive for what it is, but a place you can get an omelette, etc.
I prefer the Viand at Madison and 61st if I’m remembering right, for a greasy spoon breakfast. It used to be cash only but things might have changed.
If you’re really watching your budget, an egg on a roll from a corner vendor might be your best bet. They’re around midtown in the morning.
I find there are more interesting breakfasts if you head south of 42nd Street. I like the breakfast sandwiches at Sullivan St Bakery on 8th Ave- which has tables and counter service- but that’s pretty far from where you’ll be staying. I don’t know if the Hells Kitchen location has breakfast sandwiches.
For good pizza by the slice, I’d also head south of 42nd. I have a memory of trying to find a slice near Times Square in the pouring rain, getting soaked and eventually going to Virgil’s for mediocre BBQ because I couldn’t find non-chain pizza by the slice.
Re: pizza