Cafe Atma is great - the atmosphere is lovely and cosy and the staff are all very friendly and welcoming. The food and the cakes are delicious and their coffee is amazing - as good as Starbucks/Costa. They do all the different kinds (not just filter coffee) and have soy milk of course.
Most of their cakes are vegan and I believe all of their meals have a vegan option.
It's my favorite place for coffee/cake and for vegan food in Cardiff.
Cons: Location isn't central, Can be cold by the doors in winter