Hey,
Sunflower on Union St. is ok for some craft beers,1 cask and Clanconnel bottles last time I was there two weeks ago.They also had some bottled English ales,can't remember what exactly. It's a nice small pub too with friendly people. Some trad sessions upstairs too.
The Crown is great for cask.Plus a beautiful place to be in.
Bittles Bar has some craft on tap and bottles.Also a nice atmosphere.
The John Hewitt and McHugh's has cask and some bottles
The Kitchen bar near Bittles usually has something interesting and also does cask.
All these are in the centre and within walking distance of each other. I travel to Belfast quite regularly and while it's good for cask ales (which IS great!) it's not great for "craft" especially on draught. Oddly it's very hard to find any of the Irish craft regulars, even bottled.
Also the Wetherspoons is great for cask and also has some craft bottles but I'd advise you go for a day pint and avoid weekend nights if you value a bit of peace and quiet.
Hope that's of some help.