If your party knew they were going to have a year of downtime, what would your character do?

Pullups, lots of pull ups.  Some sort of deadlift equivalent, maybe lifting oxcarts like in Rocky IV, no excessive cardio, just building muscle mass ... all so they can get their STR up to multi(triple) class a dip into Fighter.

EDIT: maybe keep that CON maintained and synnergize with the STR drive via pushups, lots of fast sets of high cadence pushups.  So yeah, basically doing the Rocky IV training montage.  Drago, you're mine!

Depends on the character. I got one who would pro’ly be joining MidnightPlat‘s character in his exorcise routine. I got another who would be doing charity work to help an orphanage that she sponsors. I got another I made for a 1-shot (turned 3-shot) who would be doing research to help him slay undead better, and maybe some other monster types too. I have another who would spend his time inventing gadgets and another who would be playing the lead villain in every play he could. Admittedly those last two are semiretired at the moment though. But still, yeah, it depends on the character.

My current character, Getting toasted. Nicely toasted. 

One of my characters would go to a monastery and learn the arts martial. Then he could kill people with his furry paws and vicious words. 

Hm... for the active characters i have:

- finnish an essay to deliver to the academy, haunt more books about undead, learn a new language, find and script more spells in spellbook (probably offer services to pay for them)...

- literally just go next town over to know a new place, find odd jobs and bounties to follow.

- return home and train in monastery waiting for next mission.

Let’s see, I have a bunch of ancient (35-40 years of playing) epic and near epic characters that run a caravaning company and a small country. Others sponsor new adventuring companies somewhat like Acquisitions Inc.  More recent characters (5-10 years old ) run an Inn and Caravanasery on the Waterdeep - Neverwinter road, a hunting lodge a castle and community of lizadmen in a swamp, an Inn in Waterdeep, another has a mage tower in Waterdeep and helps tutor at Blackstaff tower. What would my recent (<5 yrs) characters do ( are doing as their campaigns are on hold while I’m DMing for others)? One is a guard in a quiet Dwarven community, one is a hunter and trapper,  one is a horse trainer, and the last is an investigator and sherif for a petty lording.

Assuming I knew I would continue operating in a region, as a Bard, I would go out and make contacts in the settlements in the region.  I would do this to develop an information network so when I showed up in Winterfell or Solitude I could talk to a few friends and find out what's been going on since I was last there.

I would also refine my gear to make it the best combination of gear I could use; something like the way a back packer gets just the right tent, and eating kit, and socks and boots, and ...  But in my case that would include a well made and perfectly balanced rapier for my physique.  I would also practice my instruments in the various taverns in my region and try to learn new songs from other bards.  I would seek out authorities on the lore of the region and the neighboring regions, not just for the current age but also historical knowledge, preferably from both sides.

Id also try to get in very well with a tavern owner so I would always have a home when I returned to the area.  I'd like to have a locked closet in the basement where I could store a trunk of things I didn't need "on the road" but I had collected anyway, such as my better clothes.

I might lay the groundwork to build my own tavern someday, but one year isn't enough time for that.  I might be able to purchase a piece of land and hire an architect though.

One (Thoruk, half orc barbarian) would likely wander off and get involved in some other adventures, and then wander back. He likely wouldn't notice that he planeshifted, because that's his story.

Another (Dusty the Hedge warlock, from humblewood) would spend his time entertaining and gethering stories to adapt into fire-plays.

Another (Gizmo Grayling, Gnomish Artificer) would probably get kicked out of town for blowing up a building whilst experimenting on curses and gems. It's what he does best.

Another (Gizmo Grayling Junior, autognome sorceror) would probably start writing a book on what the magical curse-gems he stole from his dad do. This may also result in a building exploding.

Miguel (human swords bard) would probably try to get rich, and come away still poor but with every crime boss in the area after his head.

I feel like I'm missing a character, but I can't place them...

Ari (half-elf rogue)- Get involved with some kind of underground group and steal stuff. 

Harmony (tiefling bard)- Create a permanent teleportation circle to the necropolis of ythryn so she can use to the mythalar if the Frostmaiden returns. Also, run for mayor of 4 towns (there’s not really 10 anymore).

 Agnomally (gnomish draconic bloodline sorcerer)- Teach a class on why dragons are not all evil.

 Breeze (tabaxi monk)- Try to find someone who will agree to race her. 

 Grace (silver dragonborn barbarian)- Find as much silver as possible. Also, keep Breeze from dying.