Bremen - Home of the worldwide known Beck's beer and of the soccer team Werder Bremen. The beautiful, quiet city has an interesting history, a lot of nature and more. City is it's own state.
Hamburg - The city with the biggest harbour in Germany. Great nightlife and a lot of things to see. Also own state.
Hanover - The state capital of Lower Saxony surprises with much things to do and to see.
Oldenburg - A smaller city to the west. Oldenburg has a nice downtown part.
There is a special ticket for public transportation in Lower Saxony, called Niedersachsen Ticket. Please read here for more information.