Hey mates, I'm Itay, from Be'er Sheva and also a Saints fan (since I traveled in Peru with people from Ringwood in 2012).
Some tips:
1) I don't recommend you to spend the night in Be'er Sheva, cause the night life are way less interesting than in Tel Aviv, especially when all the students are out of town for vacations.
2) For traveling you can also consider the buses, in many cases their schedule is much better. http://www.bus.co.il/otobusimmvc?Language=en
3) Flight tickets to Israel will be probably super expensive due to the Jewish new year. Another option is to fly to Jordan/Egypt and to cross the border.
