If you are vegetarian or vegan (or you just do not feel like eating meat on a particular day), there are a few places in the centre of Wrocław, where you can go for a meal.
1. Vega
https://www.facebook.com/VEGA.Bar.Wegetarianski.Wroclaw
It's literally in the middle of Rynek (and, by the by, so close to McDonald's!)
Food is very good & very cheap (for Western Europeans: extremely cheap). In my opinion, to this place you can go with people who aren't into typical veggie-style food; they can take e.g. a soup, or pancakes.
It's a good spot for people allergic to gluten, because they offer a lot of gluten free stuff.
The interior design is not glamorous but that's a trade-off for lower prices.
2. Machina Organica
https://pl-pl.facebook.com/Machina.Organika
Machina Organica is a perfect incarnation of what you call 'a fancy place'. It's so nicely arranged inside, with tiles on the walls that make you think of Marocco or Andalusia, light furniture, and a lot of plants.
It's a place where you can truly taste something out-of-the-ordinary - or as a less benevolent person might put it: eat weird food. (A typical guy will find nothing to eat there...)
I've been there once for a business dinner, so I cannot tell anything about the prices. It is situated in Ruska street, near Nowe Horyzonty cinema.
3. Najadacze.pl
http://najadacze.pl/
I haven't been to this place myself, but I heard many recommendations from friends! It's in Nożownicza street, in the Old Town north of Rynek.
4. Green Way
Green Way is a chain of vegetarian restaurants across Poland. In Wrocław it's in Kuźnicza street. The food is OK (I like their pancakes) and cheap. The interior is not that cosy, but it's a place to have a meal, not to go for a lunch with friends.