JBird bakery is meant to be lovely, their website says you can phone to discuss delivery although I don't think they regularly deliver. Belfast is quite small really, if someone told me they'd ordered me lots of cake I'd quite happily travel to pick it up myself! Would that be a possibility? French Village is also good as mentioned upthread.
J-bird is fantastic, they do the most beautiful boxes of mini cupcakes that are full of festive flavours and decorated brilliantly. Most important they taste amazing. They are only round the corner from me and my goto for gifts like this. If you are interested in them and are sending to south Belfast give me a pm, I'd happily play Santa and deliver them for you. French village are also v good!