I don't know about Cologne, but six nights (or maybe even 7) in Berlin makes sense. There is a lot to do in Berlin, as well as side trips to places like Potsdam. Since you're taking public transportation, I would suggest basing yourself in Leipzig instead of Dresden, since Leipzig is more centrally located as a railroad hub. From there you can quickly and easily train to surrounding towns such as Dresden, Meissen, Erfurt, Weimar, and Naumberg. For these trips, you can use a "Lander" ticket, which allows a certain number of people to travel in the area on regional trains for a set price. See bahn.de for details, or search for Lander on the Fodor's Forum. Depending on what you're interested in, you might want to cut out one night from Dresden/Leipzig and add it to Berlin. Enjoy your trip!

Generally in Eastern Germany the accommodation prices are far lower than those in Western, though of course you can get good prices in out of the way places in the West. London Prices are famously high and not matched outside of London.

So put Liepsig and Dresden on the list and possibly Madgeburg, Hannover is also possible to drop into the mix.

Trom18 has some great cities mentioned (mainly along the Elbe) and it is worth seeing if Cowboy (sorry cannot remember his exact nom-de-plume) has advice as he seems to be German based.

Hamburg room prices are out of this world (so if you do want to stay there) see if you can get accommodation out in the sticks. We stayed here last year (2011) Hotel-Restaurant Zum Eichbaum which was a bit disorganised but the food and drink was very good.

I forgot to mention salt spas. There is a historic split in the rock formation in the area which means that you can bathe in 38C thick salt water which is fabulous. Keep an eye out. Where? Bad Wilsnack.

If I had to start in Munich and end in Berlin, what bases do you suggest...Base 1 Munich, then Base 2 still a question and Base 3 Berlin. Andy idea about base 2?

Saxony/ Dresden sure is a nice base to explore a diverse region with castles, palaces, museums and nature, incl. the vineyards along the Elbe river.
Many people also like the Mosel river valley esp. during that time of year. Less tourists than the Rhine valley but maybe harder to find a base (e.g. Cochem) or it will be a bit harder to reach by public transport as that area is not too well connected to the highspeed rail network.
If you have to start in Munich but what to avoid the city (or hotel costs during Oktoberfest) you can go directly from the airport to Nuremberg. While I don't find the city itself too pretty it is a very convenient base to explore Franconia/ Northern Bavaria, e.g. würzburg, Rothenburg, Bamberg, Regensburg
Oktoberfest only affects a very small part of Bavaria re. scarce and overpriced accomodation which is the city of Munich plus the surrounding region within a 100kms radius.

If for example I had to spend my 2 weeks in the Bavarian region, landing in Munich and flying out of Munich what do you say? Is it doable using only public transport..may be I start from Freiberg > Stuttgart > Munich.

I would agree that London is very expensive and that Germany is therefore probably a cheaper option - Berlin, although it is also a capital city - is actually not too expensive a place to stay (especially when compared with London) and the great German public transport systems both in the city of Berlin itself and to surrounding areas for day trips make Berlin a great option for a base in my opinion (particularly as you are flying in and out of there). www.ferienwohnung-24-berlin.com/english.htm has a variety of accommodation across the city in different price categories which would make a comfortable place for a base for interesting day trips. I would definitely recommend Potsdam as a day trip (Schloss Sanssouci is not to be missed for those who like palaces!). The Spreewald also makes a good day trip with pretty little villages along the river. And Berlin itself is ideal for culture and museums - you could start with the Museum Island for example.