What is the best item to farm and sell for Gil?
This guide mentions a method of farming to get a ton of gil.
Hidden away in a corner of Altissia is an awesome little mini-game, arena battles. These battles allow Noctis and company to place wagers on monsters as they fight it out in a battle to the death. When you are victorious you are awarded medals that you can spend on various rewards. One of the rewards is a Great Garula Tusk. This item costs 2,500 medals and sells for 700 Gil to a vendor just outside the arena. For tips on earning the medals quickly check out our Final Fantasy XV arena guide.
This probably isn’t the quickest method in the world but the majority of it can be done while you’re watching TV or doing something else. Other options, such as Hunts, require nearly as much time and take a lot more attention. Simply place the wagers and do your thing. It’s not a difficult mini-game, I racked up about 1,000,000 medals in about 80 minutes, give or take. So in roughly an I can purchase 400 Great Garula Tusks and make 280,000 Gil. This is limitless, you have to buy all of the tusks and then sell the 99 when it gets full to buy more, which is a bit tedious. But having tried everything else, this was definitely the easiest way I found to make lots of Gil in Final Fantasy XV.
As I mentioned in the comments, Vyv's quests will give you a lot of Gil for simply taking pictures. Unfortunately, these quests are not unlimited, so this method won't get you money forever, but it will fund at least two trips to the Altissia hotel, I think.
The third and most challenging method would be to complete hunts, as these always reward you with Gil for completing them. Additionally, you'll get a hefty amount of EXP for them, depending on the difficulty of the hunt.
Since you mentioned wanting to take advantage of the 3x exp stay, I assume you also wouldn't mind saving up exp. For those reasons, I shall suggest the method I used because it not only gives acceptable exp, but also very good amount of gil. I cannot say this is the "best" way to farm gil, but I found it extremely lucrative.
First, if you also wish to farm up some exp, you will want to at least activate a food with 100% exp gain while doing this method. There are other things you should also do, but since your question isn't about farming exp I won't go into those.
For the gil farming specifically, You will want to go to the Verinas mart outside of Ravatogh mountain. The tipster there will have a hunt named "Verinas Mart Under Threat". This hunt has you kill 7 wyverns that are just north of the mart.
Using the Ring of Luci special ability "Death", you can one shot each of these wyverns, making the entire fight take roughly 20 or 30 seconds or so. Each dead wyvern drops a wyvern tail. By the end of the fight you should receive
7 Wyvern tails
Now return to the mart by either walking (it isn't far), teleporting back to your car if you parked it at the mart, or return to your last rest area if you slept at the mart before you started racking up exp. DO NOT SLEEP AT THE MART IF YOU ALREADY HAVE EXP SAVED UP)
This hunt is repeatable and I believe it gives 1950gil each turn in, or thereabouts. This in itself isn't significant, but it does add up when you can complete the hunt very quickly. The payout however is form the wyvern tails. Each tail sells for 1600 or 1650 gil each. So your banking about 11.5k gil each hunt run.
I farmed this hunt for about an hour, for both exp and gil and walked away with over 300k gil. Just make sure you sell off the tails when you reach 99, it is easy to fail to notice you have hit the inventory cap and you will loose tails.
Farm the Verinas Mart Under Threat hunt for roughly 14k gil each run. Each run takes about 1-2 minutes from start to finish.
In Altissia, near the cafe just north of the floating restaurant, there is a Justice Monsters 5 machine that you can play which costs 10,000 to start (as opposed to 10 gil which is the cost for all the other Justice Monster 5 machines around Eos).
Playing this machine with the initial investment of 10,000 gil and getting all the way up to 99 chests before quitting gives you a treasure item called "Wind-up Lord Vexxos" which sells to any merchant for 500,000 gil, which is a pretty hefty return (this item can also be used to make limit-break magic spells).
The only downside is that you have to continuously play until you get 99 chests, you aren't able to save your progress or quit early without having to start all over. It generally takes me around 40-45 minutes to end up with 99 chests.
I couldn't find an official source listing all of the prizes obtainable from Justice Monsters 5 short of scanning a strategy guide, but the following reddit thread has them listed (copied and pasted the 10,000 gil rewards from a post made by reddit user dekenfrost).
Reddit post which shows all Justice Monster 5 Rewards
Number of Treasure Chests Rewards
5 Orange.
10 Foxes.
20 Platinum Bangle
25 Emerald Bracelet
30 Centurion Bangle
35 Mystic Circlet
40 Moogle Charm
45 Legatus Bangle
50 Blue Diamond Bracelet
60 Gigas Bangle
70 Assist Suit
80 Dark Matter Bracelet
90 Onion Bangle
99 Wind-up Lord Vexxos
Alternatively, another method is to keep repeating the "Verinas Mart Under Threat" hunt in the outpost called "Verinas Mart- Ravatogh" on the far south-west side of the map. This hunt's targets are 7 wyverns, which drop Wyvern Wings that sell for 1,600 gil a piece, and you rack them up quite quickly if you keep repeating the hunt. This is a good way to farm gil and experience at the same time if you need it.