Ninian Park was about a mile from the city centre so another club could have been a mile out east or north? So Tremorfa or Gabalfa perhaps. I'm not sure how much of the city today was there in the early 20th century.
It's a shame Cardiff doesn't have a proper club in the Welsh Prem (I mean a football club in and of itself, not a module on a BTEC course*). If a wealthy entrepreneur decided to have a TNS of the south here I'm not sure he'd get planning permission for another stadium.
*Yeah I know it's more than that but I don't like students.