For our week on Lord Howe Island, we stayed at Earl’s Anchorage. Nothing on Lord Howe Island is cheap, and this wasn’t either. But once we got over the sticker shock, it was lovely. We stayed in a 2 bedroom apartment/house (it was detached, but felt like an apartment) which had everything we needed to cook, and coffee and tea provided (coffee being very important for us!). The decor was very well put together, and it felt very much a cut above a cookie cutter apartment.
It had a washing machine, and drying rack, and internet access (although not very fast). It is at the top of the hill behind the shops, meaning it is a bit harder bike ride than most places (our younger son never managed the hill without having to walk his bike a bit), but that meant it felt very much in the middle of the bush. We saw Lord Howe Island woodhens by the side of the road on the way to the shops.
Highly recommended if you want to stay in an apartment on Lord Howe.