How long are you going for and what kind of holiday do you want @AvonCallingBarksdale? Beaches, sightseeing, culture, museums vineyards, religious sites, nightlife?
If you want guaranteed sunbathing weather in October, you need to go to Eilat. There isn't much else to recommend it though! It's also half the country and a desert away from the interesting sights. It will be warm (low twenties) but not necessarily hot sunbathing weather elsewhere.
Tel Aviv has nightlife, culture and beaches. It's also close enough that you could manage the dead sea/masada/Jerusalem as day trips. Actually, the country is so small (290 miles length and at its narrowest less than 10 miles wide), you could visit most places as a day trip (under 2 hours drive) except Eilat. Personally, I would probably stay a few days in different places and end with a few days on the beach either in Tel Aviv or Eilat (if you can fly out from there). In one week, I would do Tel Aviv, Jerusalem and Ein Gedi. With 2 weeks, you could explore north of Tel Aviv or go to Eilat and the Ramon Crater).
You are spoilt for choice on places to stay in Tel Aviv. This list has a few of my favourites:
www.telegraph.co.uk/travel/destinations/middle-east/israel/tel-aviv/hotels/
You might want to visit the Samaritans in Holon (just outside Tel Aviv) or Nablus (in the West Bank) for their festival of Sukkot (a month after the Jewish festival) if you are there for the right dates.
www.timesofisrael.com/inside-the-samaritan-high-priests-fruity-sukkah-literally/
I would probably stay at the kibbutz hotel at Ein Gedi to do masada, the dead sea, spa, ein gedi oasis reserve (2 days):
www.ein-gedi.co.il/en/our-story/
I would also do at least a couple of days in Jerusalem, more if you want to spend a day in Bethlehem. The American Colony Hotel is amazing, a short walk from the Old City. Try to get a room in the old Pasha's Palace or one of the old buildings, not the new block Tony Blair's old office.
www.americancolony.com/
Places to visit north of Tel Aviv:
Netanya - great beach
Caesarea - Roman ruins
Haifa - Mount Carmel, Baha'i Gardens
Acre - crusader citadel
Rosh HaNikra - cable car, beach, grottos
Safed - mystical (kabbalah) hilltop old city with art galleries and vineyards
Tiberias - Sea of Galilee, Golan Heights
You can do organised day trips that will take you to the main sights in 2 or 3 of those places if you really want to squeeze everything in.