Is there a surface or body cavity that does not have epithelium?
Short answer
Edit with credits to anongoodnurse: As far as I know, every bodily surface and cavity is covered by epithelia.

Background
Epithelial tissue is a sheet of cells that covers a body surface or lines a body cavity. There are two types of epithelium in the human body:


Covering and lining epithelium forms the outer layer of the skin; lines open cavities of the digestive and respiratory systems; covers the walls of organs of the closed ventral body cavity.
Glandular epithelium surrounds glandular tissue.


Hence, the entire the bodily surface is covered by some sort of epithelium. Even the eye is covered with squamous epithelia (thanks to anongoodnurse for pointing this out). 

And while acknowledging that an absence of evidence is not evidence of absence, I believe that there is no surface on, or cavity in the body not lined with epithelium.


Fig. 1. Epithelial lining of bodily surfaces. source: Ternopil State Medical University