Please forgive me if this isn't exactly the right forum, but I couldn't think of a better subreddit to ask.
I think it would be possible to use such a replica as a really immersive sort of museum.
The Getty Villa is supposed to be a replica of the Villa of the Papyri, and hold the Classical collection of J. Paul Getty.
Due to its function as a modern museum, things have changed. The various rooms are not done up as rooms would have been. I think the statues in the peristyles are replicas. They've done things like incorporate a faux Greek theater into some of the outdoor space. There's a new pavilion at the entrance.
I do wish they had set up the villa closer to a working replica of a Roman villa. The layout of the building isn't great for a museum. But what can you do?
The Church of Jesus Christ of Latter-Day Saints (aka Mormon church) has a mini Jerusalem set built 60 miles south of Salt Lake City, UT, that they use to produce Bible videos. It's about a square mile in size. Source: http://www.mormonnewsroom.org/article/bible-brought-to-life-on-ancient-jerusalem-set
The set for The Ten Commandments movie (1923) recreated ancient Egyptian architecture in California and apparently was quite elaborate, but also partially demolished and buried when the movie was finished. There's been a couple of unsuccessful attempts to dig it up again.
The set of the HBO TV show "Rome" had a pretty decent replica of the Senate, Forum, and other key sites in Rome. They also tried to be as accurate as possible with the houses, streets, clothing, etc. They got a little too zealous with the reproduction and their budget got so big the show was cancelled.
They did Cleopatra's Egypt as well but I don't know how accurate it was.
There are a couple of places in Europe where Roman buildings have been rebuild accurately.
In Xanten the former Roman town Colonia Ulpia Traiana is now a archeological park with a reconstruction of a hostel, multiple houses, an amphitheatre, and city gate. All were rebuild from scratch, in situ, using original construction techniques. The bath house only has the foundations left, but the glass cover is in the shape of the old building. You can walk through most of the rest of the town, I'd estimate about 80% of original city is now part of the park, because luckily the town wasn't built over in later times (the town of Xanten is on a small hill right next to the park).
In Austria there is the Carnuntum Archaeological Park which has a similar setup on the location of the Roman fort and town of Carnuntum with a reconstructed house, villa, bath house, and gladiatorial practice area.
And finally there is the Archeon in the Netherlands which has a substantial Roman section in the park which is based on original building plans and construction methods. The buildings are not in-situ, but the park has the most reconstructed buildings of the three listed with a temple, villa, houses, bath house, and inn.