There are trains to the local capital, Nykøbing Falster, so frequently this would be the place to go for drinks and nightlife.
Goose Pub. The local watering hole. Abandon all hope ye who enter here. Dark and smoky this caters to the very local-patriotic crowd, and it cannot be recommended to go here (especially on weekends) without a local contact that can vouch for you. Fights are very common, so keep a low profile if you go here.edit
Hotel Saxkjoebing, . Offers rooms at low rates, especially off season, maintains a high standard for such a small town. Also has a restaurant owned by Claus Meyer (of NOMA fame), serves your standard Danish gourmet fair, funny note is that this hotel seems cursed, as every one in the past many years have gone bankrupt.edit
Danhostel Sakskoebing. Cheap dorm rooms, there is a minigolf course on the premises.edit