Since I became a vegetarian I've travelled to some 70+ countries. Some particularly stood out for the quality of the vegie food, as well as the range and ease to find.
So here's my top 3 of countries that are highly interesting AND vegetarian-friendly:
#3: Thailand. Fresh, tasty, healthy, cheap. Just about every menu has a sizable vegie section. But I found that if I wanted something else, I could simply ask for a meat dish to be made with tofu instead of meat. The restaurants were always willing to do it.
#2: India. A high percentage of Indians are vegetarian, which makes vegie restaurants easy to find. There are just as many "veg" restaurants as there are "non-veg", and they proclaim it boldly on their outdoor signs. So many vegetarian restaurants that I thought I had died and gone to vegetarian heaven. Common is the "veg thali", a sort of sampler plate with three or four different dishes, rice, bread and salad. Away from the tourist-oriented shops I was paying less than 1 Euro for as much as I could eat, and a drink too.
#1: Israel. Probably a big surprise for most people - it certainly was for me. Any kosher restaurant or cafe will do. Part of kosher cooking is not to mix dairy products and meat products. So when you walk into a restaurant in Jerusalem, a waiter usually asks "meat or dairy". I would simply say "dairy" and I would be show to the part of the restaurant where the food has no meat - and furthermore is guaranteed to have been prepared with utensils and kitchen equipment that is never used with meat.
So why is Israel my top choice? The sheer range of cooking styles you get in a cosmopolitan land.