For the weather I'd say; mild weather in Istanbul makes sightseeing pleasant, while Bodrum is still warm, Istanbul will be cooler but great for exploration. Bodrum, however, will be quieter, with many bars and clubs closing by mid-November.

From my experience, I highly recommend staying at the Amiral Palace Boutique Hotel in the Sultanahmet district. It’s perfect for those who want to immerse themselves in Istanbul’s cultural and historic sites like the Hagia Sophia, Blue Mosque, and Topkapi Palace, while still being close enough to Taksim for nightlife. They offer a combination of comfort and has great access to key landmarks.