I know that the eldest son takes precedence. What happens in case of someone who dies without sons? Can daughters cremate their dead father?
You can look at my answer here. It was for a different question, but it covers what you asked for.
Yes, daughter can do the last rites, but only when all the others in precedence above her are either non-existent, or unwilling to do the rites.
Even in the case that she is supposed to do it, she cannot, being a woman, do the cremation or the rituals by herself physically or directly. I am not sure about the cremation part, but for all the other rituals, I have seen the daughter authorizing another person through handing over the dharbha grass with proper mantras or sometimes the vaadhyaar (priest) himself takes the authorization and does it.
Again, this is from experience only with south Indian, Tamil iyer practices. I am sure there will be differences by region and other communities.
In the absence of a son any Jnati or kinsmen or a Sapinda can do it.
A more specific order of preference is wife > uterine brothers.
[Every rite] for the parents, such as the offering of the Pindas, should be performed by the sons. In the absence of a son, the wife should do it ; and in the absence of a wife, the uterine brother should do the same. (21)
Usana Smriti, Chapter 7, Verse 21
Women are allowed when there are no male members available.