In 2004, when I started my studies in Norway, I was issued a D-type visa (on the sticker, it said valid for: Norway+1 transit). So, yes, once you enter the Schengen zone, you are permitted to transit through a country which did not issue you the D-type visa only once. For the rest of the duration of your visa, you should not leave the borders of the issuing country.

On the other hand, having a D-type visa in your passport, you should not have any problems of applying for and being granted a regular C type (tourist/business) visa valid for Schengen zone. In general, if you travel within Schengen zone, airport/airline agents rarely, if ever, check anything else than the front page of your passport to confirm the identity of a passenger and do no bother verifying whether you abide by the visa regime rules (but once again, valid only for traveling with the Schengen zone and only when nothing important is happening and the countries suspend the Schengen zone agreement). However, it also happened to me (once in VIE) on a VIE-TXL flight, one of agents in the lounge wanted to see my visa, despite the flight being purely domestic European.

I'd suggest applying for a C visa. It is easy to justify why you need it (am in Europe, would like to see famous cities, and so on).