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Red gloves or a diamond for a rendezvous with the Gossip. The conversation thread says "Some sort of frock" but the gloves do the trick (it may take many tries to get that particular conversation thread). Red gloves can be found in Νοσοκομείο της Αγ. Λεμπιόντα, in the laundry basket in the north-east corner of the main hall. There is also usually dog tallow in the dresser on the north side of the wall in the "altar room'.
Nine (9) beers (and some Wives' Tears, unless you like staggering around!) for the drinking contest with Thaler. He gives Geralt a book (which can not be sold, unlike all other non-quest books, but has its uses).
Seven (7) beers for the drinking contest with Yamo Ryeboozer, the boozer at The Hairy Bear. He gives Geralt the recipe for Wives' Tears (Only if Geralt did not participate in the drinking contest with the drunkard in Chapter I).
Old Friend of Mine. Five (5) celandine for Shani at Νοσοκομείο της Αγ. Λεμπιόντα. Shani thanks him and if Geralt asks her for a monster anatomy lesson, sometimes a useful bestiary entry is acquired, depending on what books he has read at that point and lore he has acquired.
Old Friend of Mine. Grandma's diary (if Geralt brings Carmen) or Grandma's cordial (if Geralt brings Siegfried) or Grandma's pickles and lard (if Geralt brings Zoltan). Pick these up the first time you go to Shani's, well before the party so they are ready to go and you do not have to stumble around drunk to get them (unless you like stumbling around drunk... after all, it does slow things down).
Or any medium or strong alcohol for the drinking contest with Erkin von Blunt in Chapter III, you will need Five (5). Check the trunk at the back of Ramsmeat's house for a bottle of sodden mead. Also, there is a lumberjack in the Βάλτο who is willing to sell Geralt his possessions, which also include a bottle of sodden mead, a red meteorite (I am not sure about this one, whether or not he hands over the meteorite may depend on how many red meteorite pieces Geralt has already found) and a silver ring, for 200 . If Geralt does not yet have the Wives' Tears formula, this is also given.
It is possible that if Geralt chose not to fight Savolla in the Πρόλογος, that there is a sapphire in the chest at the back of Ramsmeat's house (the same chest that has the bottle of sodden mead). I am not sure if the two events are definitely related, but if so, keep that sapphire for Blue Eyes in Chapter III.