Loads of choice in Edinburgh! For Veggies, as stupar says, David Bann is unbelievably good... I'm no veggie but enjoyed it immensely. Hendersons not so much, I thought it was a tad overpriced and setup was generally a bit crap. My recommendations...
Fish - Fishers on Thistle Street. Upmarket fishy restaurant, never had a bad meal but the choice is fairly limited, not sure how well they cater for veggies
Italian - Vittoria on George IV bridge. There's one on Leith Walk too, which is slightly nicer IMHO, but it's that wee bit further from centre EDIT just noticed stupar recommended this too, good taste!
Chinese - The Kweilin on Dundas St is considered one of the best, but I think it's gone downhill of late. If you can be bothered heading a wee bit out of the centre, the Taste Good on Slateford Road is where it's at. We normally get takeaway, but there's a restaurant downstairs
Indian - Well worth trying the Mosque Kitchen, it used to be literally tables under tarpaulin out the back of the Central Mosque, but it's moved to premises near Nicolson Square now, not tried it since it moved, but was some of the nicest (and cheapest!) curry I've had. Also nearby is the Kebab Mahal, which is excellent, and if you can be bothered heading out of town a bit, the Clay Oven in Morningside is ace.
Turkish - Nargile on Hanover street is excellent, but you absolutely need to book.
Japanese - Koi on Potterrow is brilliant, good choice for vegetarians too IIRC, and no, it's not all raw fish heheh
Others - Howies is a small chain of restaurants, usually top grub and good VFM. Also A Room In... is another chain which does decent food, and all 3 of them have an excellent boozer attached/owned by same folks.
That's all I can think of for now. And now I'm hungry
Enjoy!