A gnome will get you 200 favor. But every giant likes gnomes for 200. There's not a special item that one giant will give you more favor for than the other giants do.
Yup, Avery834 has it right. The more expensive an item, the more favor. Makes no difference which giant. Crystalmalizing chambers (2,500 currants) are excellent: 250 favor each, WITHOUT shrine powder. Throw on EHSP and you've got 750 favor in one go.
I know there's a cap on how many XP points you can get for donations, but I was able to get ~1000 favor in one day. So if there's a cap on favor, it's pretty high.
@Splendora and Julie. From my experience the favor cap is limited to the giant. You can donate the amount of favor that it would require to get the next emblem to each giant on each gameday.
The experience cap goes up as your level increases and is not a single cap but one for each giant. If the cap is 500 for your level then you can donate 500 exp worth to each giant.
Those are my observations, feel free to offer corrections. :)
I've been trying to donate a crystalmalizing chamber with EHSP. Even if I do it first thing in the day, when I haven't donated anything, to a giant that I have zero favor points with, I get the warning message that it will put me over the cap. That would suggest it gives more than 750 favor points. Anyone know the real story there?