If you've fished long enough to know the difference between a carp and a rusty item on the hook, before actually pulling it in, I'd suggest killing the Goblin Fishers around the Knightwell until they drop a Yew rod. It'll break on pretty much anything except moat carps, but it's free, and wears the fish out more quickly than a Halcyon rod.
The new "hot" spot to fish for these is your Mog Garden. Fishing in the pond with insect balls for bait you only catch Moat Carp. Nothing else. 200 bait = 200 Moat Carp
Another nice area to catch these is in Bastok markets, with a yew rod and little worms. Can be a little slow sometimes but useful if you get 5 rusty buckets, as you can just run up the stairs and trade them in for gil and some fame. I mainly only get moat carps there, and the occasional dark bass.
The best Moat Carp spot even over Knightswell is Dragon's Aery, fishing in Fafnir/Nidhogg's pit standing just on the edge of the drop off towards Zi'tah zone. Unless your server doesn't camp Faf/Nid, there is 0 aggro and every single small "!" catch with insect paste is a moat carp. Bite rate is very high here. Cancel all "!!!" of course~ Even at level 1 there is 0 aggro at this spot since Fafnir is camped and claimed in seconds after popping; the only thing that will kill you is Nidhogg's AOE. Best way to pass the time if you are camping Faf/nid :-)
If u have tried fishing Moat Carps in Al Zahbi at the moat, u should notice that other than the moats, sazanbaligi are also good to make money. I catch 9 stacks of moat carps to turn in each day and a stack and 1/2 of sazanbaligi which sells for about 4k on vendors.
I personally favour fishing in Windurst Woods over Knightwell or port sandy.
Windy Woods - Can fish moat carps and gold carps,fishing guild is close, NPCs are nearby and gold carp sell for about 300(3.6k/stack) making it a decent side source of money.
Knightwell- No NPCs, monster bites take up your bait (a money sink), more rusties, long run back should you forget something/break rod/run out of bait.
Port Sandy- Tricolored carps are a waste of bait. And they bite more than anything else there. NPCs are nearby though. Your pick.
My 2 cents