As far away as it gets
If you manage to get as far as Al-Jaghbub, the first thing you should do is congratulate yourself. Extremely few non-Libyans ever do. However small-scale, the place is most certainly worth the visit. The oasis of Al-Jaghbub is located around Wadi Jaghbub, a river bed that is dry most of the year.
The town is made out of traditional houses, representing an authenticity very rare in modern Libya. Most of them are 2 storey, and use natural rock and palm trunks as building material. The oasis is another example of the ingenuity of the locals, and a wide range of fruits and vegetables are grown here, including dates, peppers, tomatoes, potatoe as well as grain.
Al-Jaghbub has an interesting historical aura, and was a very important religious centre in the 19th century, as well as being a centre of the Sanusiyy movement. If you are into adventures, there are more oases to be explored, as well as something as unlikely as lakes.
Eat and Sleep
No hotels or restaurants, but local authorities have good experience in helping travellers, most of the time visitors sleep in the local rest house.
Buses are running twice a week both ways, between Al-Jaghbub and Tobruk. This is expensive.
300 km northwest: Tobruk