For annuals, I like gomphrena, vinca (catharanthus) and white sweet alyssum (I just let it self-sow every year) around my daylilies. They all seem to handle my dry soil well and stay fresh looking past the daylily season. It's just a matter of finding colour combinations that don't clash. I've found them all to be very easy to start from seed as well.
Here is 'Arnold Raeker' surrounded with Gomphrena 'Audray Bicolor Rose' and a couple additional pictures showing how lovely this annual is. It grows easily from seed for me and handles my dry, somewhat sandy soil well. This particular cultivar was not very tall, but still best beside or behind my daylilies. It would certainly complement other daylilies better than Arnold Raeker, but even still I liked this combo.
I love 'Peggy Jeffcoat' with Achillea 'The Pearl Superior', though the latter flops for me as a mature plant as seen in the 2nd photo. If only it had stronger stems! For now, I've kept them together. The achillea blooms do turn brown as they age, but then I just shear the top half of the plant off. I love white, frothy sprays of blooms with most daylilies.
My garden is typically pretty packed, but I'm always adding things anyway. I tucked a few bulbs of Allium 'Fireworks Mix' in near 'Orchid Elegance' and got lucky as they seem to bloom at the same time and to my eye, they look quite lovely next to each other. I just need to get the lavender ones to multiply and move the yellow ones out of there. (I didn't get any of the white ones in my mix.
) Also blooming nearby at the same time and complementary (to me) is this Veronica 'Purpleicious' (terrible pic, but from the same day/lighting) and Goniolimon tataricum. I think all 3 would have potential with any daylilies in the pink, lavender, white range. The Goniolimon was grown from seed.
I'll have to see if I can come up with any other combinations I've enjoyed in my garden.