Severodvinsk is not exactly a tourist destination and was never meant to be such.  It was a closed city  (even Russians could get in only by invitation) for most of its existence, until about 10 years ago. Still, if you find yourself  in Severodvinsk,  your visit there can be entertaining and fun.  

The city is near Arkhangelsk (about 35 km), center of the region,  400+ years old city that counts a Fine Arts Museum, Malye Karely open-air wooden architecture museum, a few theaters, and preserved 19th century wooden houses among its attractions.  There is also Solovki archipelago that nobody visiting Arkhangelsk or Severodvinsk should miss. To get there, I recommend booking a boat or air trip to the islands with Pomor Tour (in Arkhangelsk).

Severodvinsk's own attractions include steamboat "N.V.Gogol" that goes on tours along Severnaya Dvina river banks.  The two statues of Lenin are right in the city center, on Lenin street. There is a small history museum and a theater.  From the bridge connecting the city to its island part, Yagri,  you can see a huge Severodvinsk shipyard.  Usually a few submarines sit along the sides of the river. Kurtyaevo, a village in am hour drive away, is known for its natural springs and a small  parish.

If you happen to come to Severodvinsk in winter, there aren't as many things to do.  But there is always skiing, or sampling vodka and liquors made by ALVIZ factory in Arkhangelsk, one of the 10 best of the kind in Russia. They are very good. Try "Ryabina na konyake" (Rowenberries in cognac), my favorite.

Hotels - Nikolsky Posad hotel is in the city center.  It's the newest hotel in town, about 10 years old.   Rooms are basic and inexpensive, with showers and TVs in the rooms.   Downstairs is a restaurant and a couple of bars.

Restaurants -  a few new restaurants have opened in the past few years.  Most of them have Russian food with a few Caucasian dishes like shashlyk.  

• Metelitsa, in Kvartal B area, is a cozy restaurant that serves meat in clay pots.  
• Alie Parusa, in Yagri area, serves Central Asian dishes.  
• Ostrov Sokrovisch is the newest and priciest restaurant in Yagri area, though it's still inexpensive compared to St. Petersburg or Moscow restaurants.
• Venerable institutions like Primorsky, Nikolsky Posad or Volna never could boast particularly good food, except for Chicken Kiev, but weekend crowd with all-night live music and dancing makes the visit worthwhile - if that's the kind of entertainment you are looking for. 
• Belie Nochi, long-closed restaurant in the city center, has re-opened in the same building, although in a much smaller version. Live music.
• Chaika cafe in the city center has been remodeled and offers cheap lunch specials for 40 rubles.
• The best shashlyk was found at a cafe on Oktyabrskaya street.
• Lakomka, dessert destination, is a good stop to get a sugar fix.

Clubs - to dance with crowds of teenagers, go to Yuventus, a converted movie theater, previously known as Priboi.

Shopping - go to souvenir shop on Sovetskaya street  in the city center.   They have good selection of  northern crafts (Mezen, for example) and models of submarines built at  Severodvinsk shipyard.

Transportation - to get to Severodvinsk from Moscow or St. Petersburg, fly to Arkhangelsk  on Arkhangelsk  Airlines  ($70-80 one way), then take a cab to Severodvinsk for about $10.   There are also direct trains from Moscow and St Petersburg that go to Severodvinsk, but they take 24 hours, although may cost as little as $6.

To travel from Severodvinsk to Arkhangelsk, take a cab or a bus (#133 or #138). Intra-city buses go to towns in Arkhangelsk region from Railroad station.

Enjoy your trip! Please e-mail me if you have any questions.