The Century Building is on 7th Street downtown. It's a good downtown location, I would think. You would be right in the heart of the Cultural District, a couple of blocks from Heinz Hall, The Benedum, the O'Reilly Theatre, the Byham Theatre and the Harris Theatre, so things would be actually going on in the evening in that part of town. Here's a link to information on the Cutural District --
Cultural District Map
So even if you're not a big theater-goer, the fact that they are there means that the area is a bit more active in the evening than the rest of downtown will be. Downtown living is fairly new to Pittsburgh. There has always been some, but it's just starting to be on the rise. But, since it's not been a staple, downtown overall tends to be a more 9-5 place. However, the cultural district gets more traffic in the evening. It will still likely be slower and quieter than what you're used to in NYC. But at least restaurants will be open in the evenings and on weekends for the most part. (There are sections of downtown where this is not the case.)
And it is a mere walk across a bridge from PNC Park and North Shore attractions. Additionally, Point State Park is a short walk down Penn Avenue from there, and there is a long river walk on the North Shore, so you can walk, bike, rollerblade, etc. close to home. Not that anything in downtown Pittsburgh is very far, it's extremely compact and it's all walkable. And, like you mentioned, from downtown you have access to most of the area via public transportation.