Here's some data extracted from http://na.ff14angler.com/
Note: For the Gthr data, the highest listed value is the lowest known value of Gathering that definitely works. The lowest listed value is the highest known value that resulted in an "Insufficient Gathering" message (+1). This gives the range where the minimum Gathering score must reside.
Code:
Fish: Gigantshark
Zone: Middle La Noscea
Hole: Summerford
Wthr: Clear, Fair
Time: Any
Bait: Floating Minnow (12.3%) -> HQ Merlthor Goby (18.8%)
Floating Minnow (62.7%) -> HQ Harbor Herring (13.3%)
Floating Minnow (62.7%) -> HQ Harbor Herring (38.6%) -> HQ Ogre Barracuda (39.8%)
Lugworm (50%) -> HQ Merlthor Goby (18.8%)
Gthr: ?-299
Dsyn: Chance at 100 CUL dSkill: 100%, at 80 dSkill: 70%
Loot: Sea Breeze Summer Halter (7.7%), South Seas Talisman (11.9%)
Fish: Octomammoth
Zone: Limsa Lominsa Lower Decks
Hole: Limsa Lominsa Lower Decks
Wthr: Any (Confirmed: Rain, Fog, Cloudy, Fair, Clear)
Time: 9am-5pm
Bait: (There are many valid options, but this is clearly the best)
Pill Bug (7.3%) -> HQ Merlthor Goby (20.1%)
Pill Bug (36.5%) -> HQ Harbor Herring (31.8%)
Gthr: ?-300
Dsyn: Chance at 100 CUL dSkill: 100%, at 80 dSkill: 70%
Loot: Sea Breeze Summer Pareo (7.7%), Blue Summer Maro (7.7%)
Fish: Twitchbeard
Zone: Mist
Hole: Mist
Wthr: Clear, Fair
Time: 4am-6am
Bait: Spoon Worm (41.8%) -> HQ Fullmoon Sardine
Gthr: ?-341
Dsyn: Chance at 100 CUL dSkill: 85%, at 80 dSkill: 50%
Loot: [insufficient data] Red Summer Pareo (?), Red Summer Maro (?)
Fish: Shark Tuna
Zone: Eastern La Noscea
Hole: Costa del Sol
Wthr: Clear, Fair
Time: 7pm-9pm
Bait: Spoon Worm (37.4%) -> HQ Fullmoon Sardine
Gthr: ?-347
Dsyn: Chance at 100 CUL dSkill: 85%, at 80 dSkill: 50%
Loot: [insufficient data] Summer Sandals (?)
Fish: Olgoi-Khorkoi
Zone: Southern Thanalan
Hole: Sagolii Dunes
Wthr: Heat Wave
Time: Any
Bait: Sand Leech (41.9%) -> HQ Storm Rider
Gthr: 345-348
Dsyn: Chance at 100 CUL dSkill: 85%, at 80 dSkill: 50%
Loot: Waterproof Cotton (7.1%)
Fish: Frilled Shark
Zone: Western La Noscea
Hole: The Ship Graveyard
Wthr: Cloudy, Fog
Time: 5pm-3am
Bait: Floating Minnow (100%) -> HQ Merlthor Goby (100%) -> HQ Wahoo (78.7%) -> HQ Giant Squid (21.9%)
Gthr: 370-383
Dsyn: Chance at 100 CUL dSkill: 85%, at 80 dSkill: 50%
Loot: [small dataset] Coronal Summer Halter (~5.5%), Ti Leaf Lei (?)
Fish: Toramafish
Zone: Upper La Noscea
Hole: Oakwood
Wthr: Any (Confirmed: Fair, Cloudy, Fog)
Time: 5pm-7pm
Bait: Spinner (41.7%) -> HQ Common Sculpin
Spinnerbait (40.9%) -> HQ Common Sculpin
Gthr: ?-336
Dsyn: Chance at 100 CUL dSkill: 85%, at 80 dSkill: 50%
Loot: [Insufficient data] Rose Roselle Capeline (?)
Good, easy to catch fish for leveling CUL Desynth (good for that gap between 75 and 90 skill)
Fish: Coeurlfish
Zone: Upper La Noscea
Hole: Oakwood
Wthr: Any (confirmed: Fair, Cloudy, Thunderstorm)
Time: Any
Bait: Spinner (41.7%) -> HQ Common Sculpin
Spinnerbait (40.9%) -> HQ Common Sculpin
Gthr: ?-195
Dsyn: Chance at 100 CUL dSkill: 100%, at 80 dSkill: 70%
Loot: Nothing special (just a good desynth leveling fish)
Fish: Takitaro
Zone: Western La Noscea
Hole: The Ship Graveyard
Wthr: Any (confirmed: Sunny, Fair, Cloudy)
Time: Any
Bait: Streamer (13.8%)
Gthr: ?-242
Dsyn: Chance at 100 CUL dSkill: 100%, at 80 dSkill: 70%
Loot: Nothing special (just a good desynth leveling fish)