There are few daily busses from/to Nukus - 5000 sum (sept 2016), also the busses going towards/from Moynoq (5000 sum) stops there. City has a train line. Shared taxis are around the bus/taxi station, close to bazar, towards train station. Train leaves daily to Aktau at 8:25 (25 hours).
Several restaurants are around train station and bazaar is 10 mins walk away towards west. Bazaar has basic food (fresh and cooked and other goods), way less what you can usually get at the bazaars in other cities.
Guesthouse, (Right next to train station. On your left when walking out of the station, just across parking lot. If you pass ticket office, you went to far. They have black sheep horns above the door and the sign in the window saying 'открыты'.). No registration possible. They have other meals available as they are also a restaurant. Very basic rooms, toilet outside and get ready for a bucket shower. $10 with breakfast. edit