Hotels
Vlad Inn
Reservations can be made online. They offer a free pickup service from the airport. It's a Western-managed hotel with English-speaking staff. Also has a very well-reviewed restaurant on premises. To reach the Vlad Inn, take an elektrichka commuter train out to Sanaturnaya approximately six stops outbound from the Vladivostok train station. From there, it is a short walk.
Hotel Hyundai
The height of luxury in Vladivostok, with full business facilities, swimming pool and fitness center, bar, casino, and restaurant on-site. Rooms have satellite TV and air conditioning. Online booking is available.
Hotel Vladivostok
Budget and somewhat more upscale rooms, with Wi-Fi and a buffet breakfast; there's a restaurant on-site. Online booking available with limited Russian. About a ten minute walk from the train station. It's quite an ugly building from the outside, but one side faces a nice view to the sea. Rooms are being progressively renovated, so standards vary. The hotel is now jointly managed under the Azimut brand along with the former Hotel Amursky Zaliv nearby - see the entry for "Hotel Azimut".
The hotels in the city center are targets for huge tour groups, who block out availability for weeks on end, so reserve in advance if possible.
dorms
Russian dorm rooms in Vladivostok range from awful to OK. Generally, foreigners are dormed in reasonable accommodations, but you should know exactly what you are getting into before arriving. Important things you might take for granted include: private or communal kitchen and bathrooms, number of roommates, number of clothing washers and dryers.
The Far Eastern National University above offers reasonable dorm rooms but foreigners are separated from Russian students, so if you are looking for more Russian immersion, ask them about arranging a home stay.