Nucleus instance segmentation and classification in histopathological images is an essential prerequisite in pathology diagnosis/prognosis. However, nucleus annotations (e.g., segmentation and labeling) require domain experts, and annotating nuclei at pixel-level is time-consuming and labor-intensive. Moreover, nuclei from different cancer types vary in shapes and appearances. These inter-cancer variations require careful annotations for specific cancer types. Therefore, to minimize the labeling cost, we propose a novel application that considers each cancer type as an individual domain and apply domain adaptation techniques to improve the segmentation/classification performance among different cancer types. Unlike the previous studies that focus on unsupervised or weakly-supervised domain adaptation independently, we would like to discover what kinds of labeling can achieve the most cost-effective domain adaptation performance in nucleus instance segmentation and classification. Specifically, we propose a unified framework that is applicable to different level annotations: no annotations, image-level, and point-level annotations. Cyclic adaptation with pseudo labels and adversarial discriminator are utilized for unsupervised domain alignment. Image-level or point-level annotations are additionally adopted to supervise the nucleus classification and refine the pseudo labels. Experiments demonstrate the effectiveness and efficacy of the proposed framework (jointly using unsupervised and weakly supervised learning) on adapting the segmentation and classification model from one cancer type to 18 other cancer types.