It's in the room with a circular tower in the middle and a couple of bridges built out from it just after the very first point where Ezio knocks down some masonry that will enable him to climb back up. Memory 6: There is a large treasure chest with 1597 florins in the Hall of Nero Romulus Lair. Memory 5: Kill and loot the Borgia courier after you catch him for 1500 florins. Memory 4: Kill and loot the pickpocket after you catch him for 500 florins. Memory 3: Loot the Borgia Captain for 918 florins. Most people coughed up between 11-15 florins, with occasional takings of as low as 7 and as high as 25. It breaks down roughly like this: Mission objective rewards, chests and some special circumstances (detailed below) = 5798 florins. I began Sequence 2 with 0 florins and ended this sequence with 8527 florins. Except for one chest, all of these in this sequence were small - under 200 florins - so it wouldn't matter greatly if the small ones were skipped (there were only 5 total in any case). The same with chests if any were in my path, then I stopped and picked them up. I went pretty directly from one objective to the next and pickpocketed everyone I came across while not going out of the way to do so. I pickpocketed continuously while fast-walking whenever possible (you have to ride a horse when following Machiavelli from Augustus mausoleum to the pickpocket guy, then again from the Campidoglio to the Colosseum), although I slacked off the pickpocketing slightly whenever guards were close enough to notice. I'm sure that would be too slow, however. The main thing I do is renovate as many of the shops as I can as fast as possible. I love the crossbow, so I try to gain as much money as soon as possible so I can have it. If you would like to have the info, I'd be glad to work on mapping the florin amounts in each chest, along with when it becomes available. The shop items are listed on the maps, but not the florin amount. Asaic has made maps of the whole city with the treasure chest locations shown. Locating the treasure chests that have the largest amounts of florins in them might be helpful, although because the map only opens up gradually it could be difficult to find the large treasure chests early enough. If you do any of the Borgia towers, be sure to loot the Borgia captain if you can. They're also usually found out in the countryside at night, but sometimes will venture into the city. Be sure to loot them after the courtesan mission, the one where you try to ransom the madam. The Cento Ochi are good for a fair amount of money, along with sellable items. The place to do that is the Centro district north of the river that area has the most people and they are more well-to-do than other areas of the city. Your best bet is probably doing your own pickpocketing.
That would probably take a huge amount of time too. The thieves won't pickpocket for you until you get enough of the guild challenges done. (The second most frequent point seems to be outside the Isola Tiberina hideout, although it doesn't happen very regularly I don't think.)
It would be hugely time-consuming to travel back and forth enough times to get enough money. The most frequent spawn point for them is taking the tunnel to the Thieves Guild, after completing the mission with La Volpe and rebuilding the inn. Borgia messengers are available, but they are not nearly as numerous as in AC2.