In Karelia it is the city of Loukhi and area. One of the Moscow State University marine research stations is there, and the KGB fellow regularly come there from Poyakonda to see if there are any spies there. For Karelia see http://www.staritsa.info/category/karelia/
In the Murmansk region some areas along the Barents Sea where the northern fleet is stationed are fully restricted. Ask for details.
Kandalaksha itself is OK to visit. There is a sign along the south edge of Kola that says “foreigners staying there for more than 24 hours must have a permit” but who cares. Not that I openly call you to disregard the law. My style is subversion. But there is no one there to check when you enter and leave.