Your next goal will be Lobuche, where you spend the night and prepare for your final ascent to the Everest Base Camp. There are no sleeping options for individual travelers at the Base Camp. So, you should start early morning, reach the Everest Base Camp in the afternoon and return to Gorak Shep to stay overnight.
There are not too many choices of accommodations in that altitude of 5.000m. The lodges are simple but good enough for sleeping.