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Welcome to Philly!  Food is one of my favorite subjects lol (obviously)!

Here are some suggestions.  Welcome others' input as well!

Bistro La Mignette
Percy St. BBQ
Osteria
Vetri  
Fond
Parc

For lunch, I'd avoid the cheesesteak and go for the Roast Pork with extra sharp provolone and broccoli raab at DiNic's in Reading Terminal Market.  If you're not a big raab fan you can get peppers (hot or sweet or a mixture of both, which is what I usually do).

Have fun!!

Fork restaurant Innovative American/Italian sophisticated\
Southwark Sit at the bar mix with Kip interesting mix of people
Buddahkan a scene Asian fusion
Le Virtu Abruzze Italian
Morimoto upscale sushi a scen

for dinner, there are so many great places here; I would go close to where you are staying:
Old City: Morimoto, Amada, Han Dynasty, Zahav, Moshulu (on a ship)
Midtown: Amis, Barbuzzo, Inde Blue
Rittenhouse: Parc, Zama (for sushi), many other good choices around the square

Any lunch suggestions? Center City area preferably!!
Thanks in advance!

Hello. Let us hope the snow is gone.
       On Rittenhouse square. Parc. French bistro or Rouge.
                                          Sansom Street Oyster House
            Olde City                  Amada. Spanish tapas  
           Enjoy your stay.

these are all great suggestions, especially the Oyster House, but for a true treat go to the Reading Terminal Market and get a roast pork sandwich at Dinic's.  

other great places are Dandelion, Village Whiskey and Davio's. All are primo provider approved!

I want to try Davio's in the worst way!!!!

Is that a hint? The chicken livers with balsamic glaze are truly unique, if you like organ meat.

Lol!!  I am always up for dinner!!