Presumably the LEO entry is parallel to the entry in
Oxford Duden, which I think is suspect. Oxford Duden gives for absteigen: D. (übernachten, wohnen) in einem Hotel ~ : to put up at a hotel. This entry seems fine. When you look up visit, you find
visit at a hotel (Amer.) in einem Hotel absteigen.
"visit at a hotel" sounds very odd to my AE ears. I can't imagine a situation in which I would say it. The most common way to say übernachten/wohnen in this sense would be "stay at a hotel". As a translation of "in einem Hotel absteigen," the unmarked entry "put up at a hotel" is fine for AE, too.
A Google search on visit at a hotel
, so it's certainly not a common phrase. Some of these hits were for accidental juxtapositions, such as
"is used with each visit. At a hotel of any category" or
"A typical site visit at a hotel"