As Cardiff is not a big capital city, everything is in walking distance in the city centre. The main sights like the Millenium Stadium or Cardiff Castle are just 5 to 10 minutes on foot from the Central Train Station.
Even Cardiff Bay or the picturesque town of Llandaff are only about 2 to 3 miles outside of the city centre and well worth a nice walk.
We didn't drive or bus around central Cardiff the entire two weeks we were there. You can easily walk to anything in the city - from the castles to the megaplex theaters - in no time at all. I don't recommend doing this at night, but as long as it's daylight it is perfectly safe and fun. There are no scary backalleys and it's quite difficult to get lost. So get a map and walk, you'll see more and get some exercise! That said, if you need transportation Cardiff has it all - planes, trains, taxis, and buses - all within easy reach.
When looking around the city centre you're best off walking everywhere. Even if the weather is bad (it does sometimes rain in Cardiff) you are always close enough to a shop, arcade or pub so you'll not get too wet.