from hotel jal city haneda to tokyo

we shall be in tokyo for 4 days next week and stay in hotel gal city haneda. we plan to visit shinjuku and shibuya as suggested by our friends.
1. we want to take JR train from haneda to tokyo...how?
2. any suggestion for economical restaurant?
3. what is the best time to go there to avoid rush hour traffic?
thank you

1)
Not take JR line first.
http://www.jalhotels.com/domestic/kanto/haneda/
http://www.hyperdia.com/en/

2)
What kind you want?
http://www.japan-guide.com/forum/quedisplay.html?aTYPE=8

3)
Weekday[Mon-Fri] morning rush : 7:30-9:00
Weekday[Mon-Fri] evening rush : 17:30-19:00
morning rush busier.

And visiting Shinjuku/Shibuya before 14pm/weekday or 11am/weekends/holidays worthless not fun.
morning to noon Asakusa/Skytree area best.