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Let $X^o=\mathbb P^3\setminus D$ where $D$ is the union of two quadrics suchthat their intersection contains a smooth conic, or the union of a smoothquadric surface and two planes, or the union of a smooth cubic surface $V$ anda plane $\Pi$ such that the intersection $V\cap\Pi$ contains a line. In allthese cases we show that the set of integral points of $X^o$ is potentiallydense. We apply the above results to prove that integral points are potentiallydense in some log-Fano or in some log-Calabi-Yau threefold.

On integral points of some Fano Threefolds and their Hilbert schemes of lines and conics