I used to fish there when I was a kid. The foreshore has a bed of lugworm within about 30 yards of the shore, meaning that fish are attracted by this and can be caught by a short cast. Its also rare you lose much tackle there. Your 8 year old would have a good chance of at least catching a pouting or whiting, and there is always a fighting chance of a Cod / Conger. This is a high water only mark fishable about 3 hrs either side of high water. On a spring tide (a big one) you can fish off the sea wall, but on a neap you will be fishing on the beach. Cars are no longer allowed into the docks so you will have to park by the dock security gates (near the heliport) and walk.
The Knap is OK to but I've never caught much there, and lost plenty of tackle.
It used to be easy to drive to, but docks security stopped public cars going onto the docks quite a few years ago now.
I haven't been down there this year (I now have a boat so don't do much shore fishing) so assuming access hasn't changed. Leave the A48 at Llanedeyrn roundabout and go straight on Southern Way (across Newport Rd) Then join Rover Way. Follow Rover Way as far as you can until you get to the docks gates. At this time of year I would expect to see lots of other anglers cars parked here. Start walking from here towards the sea.
there is access. i go all the time. but it has changed. it is a long walk. u have 2 walk around the bak of the new factories, which is difficult 2 explain. but plenty of people fish there. so if u do try it.. i recommend that u sit in your car, wait 4 some anglers 2 come along and follow them. easy peasy. but i have an 8 yr old and i will not take him there. trust the gents advice and fish the pier,, or easier still on the front at penarth,,,, much safer, foreshore has 2 much rubble and junk dumped there now/ .... good fishing.