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.
The centre of Cardiff is very compact and most sites of interest are within the easy walking distance. Even to reach the Cardiff bay area requires just 15-20 minutes of slow walk along the Lloyd George avenue. Since the hotel I stayed in was located in the city centre I did not use any other form of transport other than my feet.
The only obstacle to walking are some strange installations at most pedestrian crossings that include a small "island" between the road lanes and some handrail barriers that should stop you from stepping onto the road. Plus, the pedestrian traffic lights are not coordinated and it takes ages to cross the street regularly. No wonder most locals choose other places to run across the street!
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.