In my opinion, The York isn't as good as bc was at its best. That's more a reflection on bc than The York, which is a solid restaurant if a little inconsistent. I've had some good meals there and some kind of flat meals there. Definite "scene" kind of place with pretty uncomfortable seats.
Citronelle is picking up this mantle. I've only been once, but it's very good. Its sister restaurants are Lemon Grass and Bistro Elephant. Not sure Citronelle is at that level yet, but the food is executed well and the space is beautiful.
Keeping it in the area where the OP is staying:
I appreciate someone's 317 on Montgomery mention. I love this place, which is always half-empty when we've eaten there. It's on a quiet block across from the YMCA, so there are occasional street people and apparently random walk-in traffic doesn't find this place. So I'm glad they're still in business. But the food is good.
The Mission is solid. I think they call themselves "Pan American" - pretty much just a Latin-influenced place in an old church with an Underground Railroad history. Nice, not my first choice, though.
The Fish Friar is terrific. Very short menu, excellent beers on draft.
With Love has been doing great things, but from a culinary and educational standpoint (it's a restaurant start-up incubator run by OCC; every six months they give a different person a chance to run the place and learn the biz with a new menu). Haven't tried this Palestinian iteration yet, but hope to get in there in the next couple weeks.
I like Apizza a lot. Can be tough to get a table. Buzzy place but pleasant space. Pasta dishes are usually good, and I've liked the pies I've tried (they had a spicy salmon nduja last fall that was crazy good, not sure if that's on the menu right now).
Everyone likes Francesca's...it's almost so overrated that it's underrated because it's so good, if that makes sense. Food is good across the board, prices are reasonable, outdoor space is incredible and the inside is nice enough too. Service is shaky - some servers are very personable (there's a guy named Pat O'Brian who's hilarious) and some aren't, and the hostesses often have a kind of townie standoffishness...it kind of has the vibe of a regulars place in some ways, but it isn't, and it's worth a visit.
XO Taco is a new place between downtown and the hill, just opened last week. Haven't been but am hearing good things.
The Stoop is a year-old restaurant/bar/bakeshop on West Fayette in Armory. Restaurant's a mixed bag. Bakery is phenomenal. This is worth a stop.
Defi Cuisine Corp. is two blocks up from there. The menu doesn't grab me, but everyone I know who's been is raving about it.
A little farther afield, Riley's is awesome. Same deal with the Cider Mill, so underrated for a random little joint, though I didn't really care for their summer menu this year. Counting down the days til they break out something new for fall.