Tipped

My personal preference would be to walk a few blocks away from Shoreditch to Coffee @ Whitecross Street - great vibe, comfy chairs and couches, and free wi-fi. I would review it on Tipped, if I could figure out their address. The coffee is great - the only downside is that lunch times, especially on Friday, get very busy because of Whitecross Street Market. There is also the Coffee @ Brick Lane, but I prefer Whitecross myself.

You could also try The Bean on Curtain Road - not my favorite, but many people like this place and they have wifi.

MAcondooooooooooooooo - not free wifi but there is wifi that you have to pay a little bit for. Bar Music Hall is pretty comfy and has free wifi. Prague has a couple of sofas and free wifi as does Old Shoreditch Station opposite (plus hot barmaid / barristas) - oh and both the Coffee@'s on Brick Lane have sofas and free wifi.

@AndyM - I'll get that Coffee@Whitecross listed for you

Doesn't Hoxton Square itself have free wifi? I thought I saw a banner announcing this recently. Weird for a square to have wifi - maybe I imagined this.

Two more that were endorsed by a barista friend and coffee expert, though I haven't tried myself.

http://www.tipped.co.uk/listings/224507/Taylor%20Street%20Barristas

http://www.tipped.co.uk/listings/224506/Taste%20of%20Bitter%20Love