I just saw your post! I'm not in Edinburgh either. I live in Falkirk, which is more central Scotland. About 30 minutes away from Edinburgh.
I home ed my 4 (they're 8, 7, 4 and 16 months). There is a home ed group in Edinburgh. I've been trying to get some details on it, but it seems to be like a secret society or something! No one wants to tell me anything or let me in!!! Apparently they meet weekly (i think) and they have lots of outings organised too. I help organise a home ed group out in Falkirk. We meet in a church hall over winter once a month. We meet outdoors more often in summer months. Most of the children that come are pre-school aged. There is lots going on in Glasgow too. There is a weekly play club in Hyndland (which is easy to get to on the train, but might be a bit of a long journey from Edinburgh). They have lots of workshops at museums organised for the next few months. There's also a group that meets at North Queensferry, which is just a short train trip away from Edinburgh over the Forth bridge. I've only been there a couple of times, as its a bit akward to get to for me.
Here's some home ed links for you:
http://uk.groups.yahoo.com/group/falkirk_home_ed/http://groups.yahoo.com/group/scottishhome-ed/ (this is the main home ed list)
http://uk.groups.yahoo.com/group/northqueenshome-ed/
Hope this helps!