If you plant caladiums outside, you'll have to dig them up in the fall. I just planted mine right next to some daylilies, in fact :)

I thought daylilies needed more sun?

What do you do with the caladiums after you dig them up in the fall? Are they bulbs that you can just save and replant in the spring?

Yes, dig up, store, and replant next year. I will do that with my dahlias as well. (I put little rock rings around them so I can remember where they are.) If you grow them in containers, you don't have to dig them up - just store them in the container.

(I have unknown daylilies growing in shade. I did not plant them and they do not seem happy where they are as they have produced just one flower stalk (scape?) so far from a row of about eight plants. You might want to try asking in the daylilies forum if nobody here has an answer.)

Daylilies do need sun to flower. Ive experimented a lot over the yrs., I would say in general you dont get any flowers in total shade, a sparse few in dappled shade, more in part sun, a lot in 1/2 day or more. Except if its a really hot all-day sun then thats no good either, they seem to fry under those conditions. Those are my observations anyway.