Belavezhskaya Pushcha National Park headquarters runs four hotels near the park entrance, unimaginatively dubbed Hotels No 1, 2, 3 and 4. The newest and best of these is Hotel No 4, which has huge, supremely comfortable rooms to go along with a 25m indoor pool, darts, ping-pong and Russian billiards. The other three hotels are older and slightly cheaper but still not bad.
All have restaurants and there are several additional cafes near the park entrance. It's best to call ahead to reserve a room, although if you just show up on a weekday the hotels should be able to accommodate you (weekends are a different story).