Driving from Haneda to Izu, to avoid traffic?

What is the quickest driving route from Haneda International terminal to Atami (JR station say),if we leave Haneda around 3pm on a weekday, how long approx and how much are the tolls ? Google map has a suggested route which is supposed to take 1 hr 45 mins "without traffic" (106km) BUT I am asking for any suggestions because we drove in January a few years ago leaving Kamakura around 4pm and Google map said it would take 1.5 hrs to Tokyo Akasaka but it ended up taking over 3 hrs with heavy traffic most of the way, and I remembering wishing that I had taken the Tomei expressway instead, so would appreciate any suggestions.

HND to Atami around 2h15min maybe via Yokohama,Hodogaya and Tomei
Toll roads(not only one) fee about 3000Y total
and fuel fee around 1200-1500Y/8-10L. (not include rental car fee)
BUT no big saving money not recommend.(depends on group numbers)
Avoid traffic take a bus or trains cheaper usual except by Shinkansen.
http://www.hyperdia.com/en/

If really want drive "VICS" helps you.
http://www.vics.or.jp/english/vics/index.html
No VICS-less navi in Japan major rental car campanies car
Toyota,Nissan,Nippon,Times,Orix,Eki-ren(JR) and more
but more smart navi by FCD need to join and member ship fee usual.
Internavi,G-Book,CarWings and more are so. (FCD : Floating Car Data)

Google map "traffic" info also works on yr cell phone no option fee.
But Google map is no navigate function with just checking real time.
http://googlejapan.blogspot.jp/2011/12/google_09.html
http://en.wikipedia.org/wiki/Google_Traffic
https://support.google.com/maps/answer/3093389?hl=en

HND Int'l terminal �� (metropolitan expressway) �� (Yokohama Shindo) �� (Hodogaya BP) �� (Tomei Expwy) �� (Odawara-Atsugi Road) �� ... �� (Manazuru Road) �� ...Atami

Got it thanks, so basically follow Google map and I think the GPS Navi in my Toyota rental car will say the same. Guess I was unlucky with the severe congestion the last time.

Last time you left at 4pm on a weekday and took surface streets? That pretty much guaranteed that you'd hit rush hour traffic. Leaving earlier and sticking to the expressways this time should help a lot.