One unique aspect of being Israel is the Sabbath. If you are planning to stay beyond the symposium, you need to take into account that most businesses work half of the day on Fridays and are completely closed on Saturdays. Same is true for public transportation, which is unavailable on weekends.
The strictness of Sabbath observance varies among municipalities. Jerusalem may be overall more strict, while Tel-Aviv or Haifa more liberal with many restaurants open and some public transportation options available. In any case, you can still hail a taxi on weekends and you can obviously drive (other than through the ultraorthodox neighborhoods).
It is relatively warm in Israel. The average temperatures in Jerusalem in October are around 20-28 C. It might rain, but this is highly unlikely.