My husband and I are going on a delayed honeymoon to Mykonos and Santorini. I think I have Mykonos settled at the Argo Hotel, but would be open to other suggestions. We are looking for suggestions in Santorini with a preference for Oia. We normally backpack in Europe and used to staying at hostels.
Not sure what moderate price means to you, but for a honeymoon, I would recommend the Aspaki Hotel. Fantastic location in Oia pretty much at the top of the island with incredible views of the volcano, caldera, and both ends of the island. It's not cheap, but for a honeymoon, it would be perfect. Look on tripadvisor.com/aspaki for great personal photos and reviews. We loved it.