Israel for 3 weeks

You are jumping around too much. Combine your two Tel-Aviv stops to one at the beginning of the itinerary. Also you don't need 6 nights in Tel-Aviv - 3-4 is enough and you should add extra time in the Galilee or go to Petra in Jordan. You also don't need 3 nights at Massada - 1 night is enough with careful planning or you could take a very efficient one day sunrise tour from Jerusalem:
http://abrahamtours.com/theme/israel-tours/

You don't say when you are coming. You definitely have to book in advance in the summer or other high seasons. Also what type of accommodation are you looking for and what is your budget. If hostels - here are the official hostels (open to everyone) and the independent ones:
http://www.iyha.org.il/eng/
http://www.hostels-israel.com/index.asp

Public transport is very good in the cities and between the main cities and towns. you can check the schedules for buses:
www.otobusim.co.il
and trains:
http://www.rail.co.il/EN/Pages/HomePage.aspx
Public transport is inefficient when you try to visit the smaller sites in the outlying areas, particularly in the Galilee and the Negev. It is a good idea to rent a car for 2 or 3 days - you will see more than you would in a week by public transport.

Please indicate what your interests are: history & archaeology, religion, nature & hiking, clubs & pubs, etc, etc

Agree with mbgg.
And you don't have to sleep one night in Nazareth (unless you absolutely want to). Use Tiberias - or any other convenient place (such as Rosh Pina) - as your sole base for the Galilee, making one less accommodation switch.
Same for Bethlehem. An easy half day trip from Jerusalem. You don't have to sleep in Bethlehem unless you really want to.

Hello,
I would suggest reducing time in Tiberius (not much there) and Masada and spending more time in Haifa. Us Haifa as a jumping off point for Akko (Acre) and areas around (including Nazareth) as they are easy to get to while staying in a hostel in Haifa. That way you do not have to carry your pack etc. and look for accommodation.

You definitely need to book key accommodation (Jerusalem, Haifa) in advance. Getting to Jericho from Jerusalem is now easy. Departure is still from near the Damascus Gate. You can even combine Jericho and Bethlehem quite easily in a day despite what locals will tell you. See my earlier posts on this.

While in Jerusalem seriously consider doing the Hebron dual narrative tour organised through Abraham Hostel. Gives you a great insight into the conflict there as you will meet both Jewish settlers and Palestinians and hear both side of the story. It was probably the highlight of my trip to Israel.
Cheers