We have 6 places to stay in and around Gili Gede.
The township of Pelangan is the closest serious point of civilisation near to Tembowong, from where regular boats can take you on the 10-30 minute boat ride (depending on destination) to Gili Gede. If you arrive late or in inclement weather or for whatever the reason want to overnight on the mainland, the two closest options to the boat "harbour" are Bola Bola Paradis and Palm Beach Garden. Neither are great lodgings, but both are friendly and will do at a pinch.
Further east from Pelangan and Tembowong you’ll reach a cluster of guesthouses and homestays a little before the road heads inland and turns to dirt. The road splits in two, with the right track leading to the fishing village of Bangko Bangko and the left veering to Desert Point, arguably Lombok’s premier surf spot. In season it is possible to stay at Desert Point itself, but out of season most places close and the options are strung out along the coastal road that faces out to Gili Asahan and Gili Goleng. As we visited out of season, the only place we could find that was open was Desert Point Lodge, which sits more or less opposite the boat landing for Pearl Beach on Gili Asahan.