We have found a delightful veggie restaurant in Altea Town (not in Old Altea but just the sea side of the railway.)
The menu del dia is about 11 Euros and was pretty amazing.If you are uncertain what to choose for the starter and the main they offer the option of going 50 - 50 which was great for us as our Spanish is still somewhat limited and gave us half a chance of liking something. As it turned out we liked the lot and the pudds were also a very high standard.
We tried it again at dinner time but neither of us thought it was quite as good as the lunch menu.It was more expensive and there was a huge choice - perhaps too big a choice for such a small place.We may have been put off because it was very quiet that particular evening.They have not long been open and are still building up their business.
However if you are in Altea at lunchtime its a real treat,the decor is modern and there are nice touches with candles,incense and artwork and the waitress who served us was sweet and charming. 
The address is Calle Ferrocarril,6
03590 Altea
Tel 96 584 33 77.