The restaurant that zuriga1 refers to as 'Mint and Mimosa' is actually called 'Mint and Mustard'. However, the chef he refers to who opened Mint and Mustard, Anand George, is no longer associated with it. He does however have a restaurant called Purple Poppadom which is in the Canton area of Cardiff and is well worth a visit. Mint and Mustard is still worth checking out. Another similar 'higher end Indian' option is Moksh in Cardiff Bay. Purple Poppadom is my favourite of the three.
The other restaurant zuriga1 refers to, Patagonia, closed several years ago as did Le Gallois whcih is in the old link referred to by rrems. The Walnut Tree also mentioned is in Abergavenny rather than Cardiff but well worth a visit as is Stephen Terry's pub The Hardwick in the same area.
Have not personally been to Vegetarian Food Studio that Harters mentions, but my wife has and likes it a lot. Other options worth considering are Bangkok Cafe in Canton for Thai and Mr G's Soul Kitchen in The Bay for Jamaican goat curry and jerk kitchen. There's a Malaysian restaurant in Cathays called Cafe Malaysia that I've heard good things about but not been to.