My hexblade sorlock is trying very hard to set up a permanent shrine to his god out of some old ruins.

Thing is, there's a lot of tourism at these ruins, they're basically like Stone Henge, so he draws them in and uses them as sacrifices. Haha.

It's been a long time since characters at my table have had any downtime, since we've not actually been playing much D&D at the moment (our regularly scheduled game is current HackMaster, wherein the characters have been using their downtime to recover from injuries and train, because that's the kind of thing that regularly happens in that rule system).

We did just the other night finally get our somewhat randomly scheduled and only run occasionally side campaign of D&D back on the table after a semester-long hiatus (my wife having finally finished the online courses that required every spare ounce of her focus and time for her to pass), and downtime is coming up soon.

Thanks to the newly revised downtime rules, the party is likely to go do some shopping for magic items as they have a couple wizards that would like to expand their spell repertoire, and the assassin in the party might just go do some pit fighting for the sake of that being an officially covered option and not out of line for the nation the characters will be briefly visiting before going on their next big adventure.

The players in my game are currently rebuilding an abandoned town and trying to attract settlers. They were gifted the town and surrounding land by a Lord who couldn't pay his bills. Now my group has pretty much ignored all there other commitments and are running with this. I spend about an hour at the beginning of each session discussing their plans for the town.

It the town of Uluvin, just north of Secomber. Except in my game all the occupants were run off by bandits and goblins when the lord of the area couldn't afford the men to keep it safe. 

My party in a campaign I'm in just had a year of downtime. We set up a base for us out of a dragon's lair, I created a shrine to the members of the original party, of which I am the last. Sold a good amount of high level spell scrolls, made some good cash. Bought some magic items. Other party members did about the same, some did regular old work and such. We'll be meeting our newest member next session, because the other OG party member that had survived was killed by the dragon whose lair is now our base. Other than that long downtime, my character usually tries to find out who killed him (he's a god-touched skele) to track them down and exact revenge. 

My Homebrew campaign also has a natural break and the players chose to take a year of downtime:

Character A:  looking to buy and make some magic items.

Character B: researching demons, being a travelling cleric to small towns, 

Character C: bribing a red dragon they defeated and let live.  Starting a business.  

We are moving into a new stage/story arc and this lets me give background info and set the stage for new arc.  Milestone leveling and the characters just advanced to 12th level and this is the first time they were not saying from one place to another in a relatively small part of the frontier.  Now I move them into a few large cities, and prepare moving into new parts of the world.   

We have our own Keep that we rebuilt and are the Lords and Ladies of. However my Wizard has joined one of the Mage Guilds in Waterdeep and has started building her own Shield Guardian (after first making a Homunculus the old fashion way via crafting). She also has an apprentice who is terrified of battle (has an Abjuration wizard to her Evocation spec).