From Bima you can take a bemo (around 15.000, last one 5 pm). This will take you to Sape. Iif you need to go to the ferry, ask for Labuhan Sape (that's the pier). You can also charter a bemo for 200.000. Just make sure that they won't put you onto another cramped bemo after 10 minutes...
Warung Barokah, Jl. Pelabuhan Sape (Next to Losmen Mutiara. If you come from the ferry it's on your left hand, just after you passed the gate.). Nice clean Warung. Serves Bakso and Soto Ayam. Comes with a big plate of plain rice.10.000. edit
Arema Sape, Jl. Pelabuhan Sape (500 mtr. from the harbour gate on your left hand), ☎ 037471015. This place serves a lot of fish dishes, but also mie goreng and nasi goreng (not on the menu, just ask for it). There is also an internetcafé inside if you need to spend time, waiting for the ferry. edit
Losmen Mustika, Jl. And. Pelabuhan Bugis Sape (If you walk from the ferry onto the pier, it's about 1 km. further on your right hand, just into a small street. Look out for the sign on the corner of the street), ☎ 037471227. checkout: 2pm. Nice losmen, about 1 km. from the harbour. The rooms for 75.000 have fan and squat toilet, the ones for 150.000 have AC and Western toilet. The beds in the AC rooms are better then in the cheaper ones. They serve breakfast (not included) and dinner, if you order it 1 day in advance.Fan 75000, AC 150000. edit
Losmen Mutiara, Jl. Pelabuhan Sape (Just next to the harbour gate), ☎ 037471337. edit
Hotel Mantika, Jl. Pelabuhan Sape (Just next to Losmen Mutiara.), ☎ 037471178. 150.000 - 250.000. edit
Losmen Nusa Bajo, Jl. Pelabuhan Sape 4 (This losmen is not on the pier like the others, but about 2,5 km. from the harbour. If you walk from the pier to Sape, it's on your left hand.). It has basic cheap rooms, with bathroom inside. The bathroom includes a squat toilet and no shower... 50.000. edit