Time spent while carousing costs upkeep equivalent to a wealthy lifestyle. Roll d% + character level. See table on page 128 of the DMG.
Craft nonmagical objects at a rate of 1 day/5 gp of value. You may maintain a modest lifestyle for free or a comfortable lifestyle at half cost while performing this activity.
Gain Renown (DMG)
Spend a number of days equal to your current renown x10 to gain 1 point of renown in an organization.
Practicing a Profession
Maintain a modest lifestyle for free, or a comfortable lifestyle if you have gainful employment. If you are proficient in Performance, you can put your skill to use to maintain a wealthy lifestyle.
After three days, make a DC 15 Con save. If successful, end one effect on you that prevents you from regaining hit points OR for the next 24 hours, gain advantage on saves vs. one disease or poison currently affecting you.
Perform research for 1 gp/day. Knowledge gained depends on available resources. Investigation or Persuasion checks may be needed.
Sowing Rumors (DMG)
Spend 1 gp/day to spread a rumor, which takes a total of 2d6 days in a village, 4d6 days in a town, 6d6 days in a city. At the end of the days (must be continuous), make a DC 15 Deception or Persuasion check to shift community attitude one step toward friendly or hostile.
Gain proficiency in a language or set of tools. This takes at least 250 days and costs at least 1 gp/day.
More Involved Activities (DMG, pg 128)
Building a Stronghold
Crafting Magic Items
Running a Business