Eating out in Edinburgh should pose no difficulties other than that you might have to wait to get a table in your restaurant of choice especially during peak tourist season. There is such a vast array of cuisine, with something for every budget and most restaurants nowadays offer some choice for vegetarians and vegans on their standard menus although being a student city there are also plenty of vegetarian and vegan restaurants around.
In the old town and near the castle wheelchair access can be a bit of an issue because of the old architecture of the buildings.
Worth noting:
A nice touch in Scotland is that tap water is served without charge and is quite pleasant in taste.
Sometimes for larger groups a service charge is already added to your bill. Otherwise a gesture of 10 - 12.5% is normal.