Other 'easy' downtime things to do (from Xanathar's Guide To Everything, with me arbitrarily modifying results to fit Aesithas), mechanically, are...

'Work For Wages In Town' to get more pocket money

'Carousing', which would let you learn of anyone else of importance in the city you may have not already met.

'Religious Service', which may earn you the favor of the Clergy for more broad requests.

'Training', which would be a longer-term thing (which can be broken up across visits to Fenhall) to gain other Language/Tool proficiencies over time.

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Gen, Regis, and U'Nunlo are mostly inseparable after their meeting. Rarely they can be found without U'Nunlo in direct sight in the Palace Garden, though they also go wandering the city streets At-Large and can be found often in the Market Plaza; now that they've been cleaned up and Gen given a new dress, they don't seem to be looked down upon as much. U'Nunlo either cannot be found, or for those of you particularly desiring to hunt them can be found on the outskirts of the city, foraging or communing with nature in the rare times they aren't with the kids; otherwise, they don't appear to leave the Palace Garden.

Tomas Smithson can be found anywhere and everywhere; the big city is new to him. The palace is new to him. He's often in the company of Ser Pyke, but also appears to feel an obligation to do some 'honest work that isn't hittin' things' and frequents the Smithy in town to help out. He also weekly visits the Temple to offer reverence to Noffe.

Alison and Crimson do not leave the palace, and Crimson remains silent and judgemental and cloud-like as he maintains his vigil over Alison. Alison, meanwhile, appears to practically live in the Fenhall Library, located in the base of the high tower, and Mildred appears to make time to come speak with her regularly.

Pyke is always busy, but also claims that he can always make time to help out or chat so long as people don't mind walking while they talk.