Great burgers at Burgatory and Hyde Park has the cloth napkins and early bird dinner special before 6pm. Both located between the football field and the baseball park and very walkable from the north shore hotels.
A little more of a walk would be up to Manchester neighborhood and the Modern Cafe and Nicky’s Thai Kitchen. Manchester is less than a mile northwest from the Hyatt Place hotel.
And directly north would be Allegheny Commins and the Federal Galley with several smaller food court eateries. Beyond the Commons there is 40 North on North Ave which had some great sliders on the bar menu when I was there last winter.
Tell the wife welcome to the North Side and hope she has a nice visit.

Is there a burger called a pittsburger?

The Strip District has a few good spots. My favorite is Little Bangkok in the Strip. Really good Thai food cooked by a friendly family. (Unweird mentioned Nicky's Thai Kitchen - that's also really good Thai.)

Roland's (also in the Strip) is a Pittsburgh favorite.

Condado's Tacos on Liberty Avenue is pretty good - and they have good margaritas.

Proper Brick Oven & Tap Room is pretty good and has a good beer selection.

If she really wants a Pittsburgh favorite, Primanti Brothers might do the trick. It's not in my Top 30 places to eat, but I have friends who travel to the city and will eat lunch there every day.

There are also a few really nice (and Expensive) restaurants on Mount Washington - which has spectacular evening views of the city. This would require a rental or an Uber to get there.

Let me know what she decides to do and if she likes it.

it's on Mount washington also North Shore Tavern
North Shore Tavern is Pittsburgh’s newest steakhouse and premier destination for delicious food, cold beer, and love of all things baseball. Located on Federal Street directly across the street from PNC Park,

I used to do their advertising when it was a Chuck Muer restaurant. Ages ago!

If she's walking around the North Shore (North Side) there are several nice restaurants between the stadiums, as mentioned in the other posts.

If she walks or drives over a bridge, she's quickly in the Downtown area. I would suggest she try the Market Square that's mostly a walk-around area filled with small interesting shops and restaurants. Market Square is easy to find next to the all-glass PPG Building.