This was my first time staying in a private villa, and it's surprisingly nice.
Literal
This-time for-the-first-time private-villa [at-に] stayed [but-が], this [topic-は] quite good is-[polite-です].
Travel review. はじめて ('for the first time') uses the adverbial form of 初める. プライベートヴィラ ('private villa') is a loanword from travel/real-estate marketing. なかなか良い ('quite good, pretty nice') uses the intensifier なかなか for positive surprise. これが at the beginning of the second clause is a topic-shifting 'this one' emphasizing the thing being evaluated.