Regularly visited the Greenhouse when I lived in Graz and it was my fav café for good reasons: It's a very cozy place that has a huge upstairs area with standard tables and couches. The staff is friendly and the coffee delicious. Moreover, they offer tasty desserts and vegan cuisine (though I've never tried the latter myself).
It's important to know though, that it's a self-service place, so you'll have to go downstairs to order.
If you are up for a cup of coffee (and maybe a good book), check it out and let the time fly by! Also good to know, they have an awesome vegan brunch buffet once a month.