The Sanctuary of the Zi'tah is probably your best bet for farming Thunder Elementals. Not as low level as the ones in Carpenter's Landing, but it's almost always stormy there and they spawn in a fairly small area.
Thunder Elementals spawn all over Carpenter's Landing in the outside areas around the river. Just wait for Lightning weather and you'll walk out with 5 clusters in a couple of minutes.
I farm lightning clusters a lot, i go up to floor 10 in delkfutt tower and get them there, i can also kill the pots for mercury and magic pot shards as a bonus. Plus Mimas spawns every 15 mins for a chance at a 8k npc great axe. Not a bad earning there.
Best place I found recently is Vunkerl Inlet(S) hear the Campaign fort, especially during double bolt weather... Right after I kill one elemental another one pops, and if not I kill crabs for sushi meat.
I spent about 12 hours on lvl 10 of Delkfutt's Tower and raked in 6 stacks of Clusters as well as 3 Giant Moth Axes from Mimas, and 3 chests of gil. All in all, 262,133 gil made on that run.
i disagree the best place is upper tower of qufin, the lighting weather spawns like every 5 min and 4+ spawn on level 10 and a few on lvl 9, inaddition it's near jeuno and gigas drop nice gil. i would recomend to be safe, any one below 50 ish (depending on job) should dou with someone. i rake in over 3-4 hours 12+ cluster douing with even shares and 2k gil from gigas