Just off hand a few money sink ideas that involve side quests:
1) A political line that involves having a high intellect, a high stealth, or loads of money to bribe officials and individuals, in order to finish a quest line with the optimal reputation.
2) A small house is found somewhere along a non-critical path and the player finds a troubled family in need. Player can decide to ignore their need or help provide for them. This is both costly and time consuming - in return, when the. say, father recovers from his illness/injury, they provide some sort of persistent benefit to the party (regular buff foods, or the offer to work as a guard/manager of your stronghold). The benefit does not necessarily have to be a net gain to the player, but is simply a question of what the player values emotionally.
3) Obviously expensive items can be a significant money sink. I feel like this is an obvious one.
4) Becoming a backer of a rebel cause (or it's rival), while staying in the shadows. This means providing both financial as well as perhaps more shady assistance. Winning the cause means a town (after the rebels win or lose) becomes hostile or friendly to the party, and becomes a hub for trading/rest near a perhaps farther from friendlies location, giving it strategic meaning but not forcing the player into the option.
Just a few ideas.