I'm certain that they do not reincarnate as soon as they die.
So where do they stay until they reincarnate?
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As per the Yogavasistha Ramayana,
The householders who perform good deeds go to dhumAvimAni devatas, then to rAtri devatAs, then to Krishnapaksha devatAs, then to DakshinAyana devatAs, then to Pitriloka devatAs and ultimately reach chandra-loka and stay happily their so long as their bundle of virtues is not exhausted.After that, they again return to the earth via Akasha, Vayu, dhumra and megha.As rain they reach the earth and enter into various corns and when eaten by jivas, they enter into jivas to be born again. (Pranava-prema-piyusha, page 317.
So those who are to be born again basically resides in the Chandraloka.