Here's some ideas for downtime actions

There seems to be a little vagueness about what you can do with downtime actions, so I'll give a few suggestions and comments here. Firstly, there's not too much in the way of concrete rules, since it's more about the plan or idea that people come up with. OTOH we'll decide some issues with skill rolls - so for example if someone wants to make money as a musician, we'll make a skill roll and use that as the basis for how much money they earn.

Some things people might want to try:

Joining one of the magical societies that has a public face and accepts members with some requirements or conditions:

Flame Society (all you need to do to join the Flame Society is swear loyalty to the leader)
Far-Talking Guild (there's a test to take)
Aquifer's Guild (you need shedloads of cash and to be a woman)
Catholicon Guild (healers - you need to pass an exam)
Children of the Transcendent Mother (you need to survive an orgiastic ritual - they teach beserker body magic)
Alchemists
Wardens (Warding and Protective Magic & Blessing)

Stonecutters

Investigate the magical societies that are a bit more secretive -
Sandwalkers
Weathermongers' Guild

Animal shifting
Demon-summoning cults
Assassins guild
Dream Merchants - part of a religion - buy and sell elements of dreams
Curse-makers - lepers

Barbers - everyone knows that the barbers of Susarra have some strange magic, but they keep things pretty close to their chest

Mysterious rat worshipping Cult

Try to earn some money

You need to suggest a plan - it could be practising a trade, selling dreams, working as a leg breaker for a criminal gang or fight in the Arenas.

Try to make some contacts
Again, give us an idea how you're going about this

Try to track down a mastercrafted weapon, or alchemical products

Investigate a loose end from an adventure
And really, anything else you can think of.