Budapest is a major city and there are lots places for vegetarians to eat out or buy vegetarian products. Here is a list of vegetarian restaurants - www.strudeldoo.com/vegetarian-restaurants-list/Budapest . As well as these you will usually be able to find vegetarian options in Sushi, Indian and Italian restaurants. For example, "Wasabi" (near Nyugati station) or Shalimar Indian restaurant (on Dob Ut.).