We visited the ASTRA museum as a family with two small children aged 6 and 4 - we all had a fantastic day out there.
We checked with the tourist office in Sibiu and you can take bus no. 13 from outside the train station to the museum, which is only 4.5 km from the centre of town. However, the train station was not very convenient from where we were staying and there are generally two buses an hour, and it was hot, so we took a taxi which cost 15 lei or just under that.
It cost 20 lei for us as a family to enter the museum; I believe children of 6 or under are free. It is a beautiful and enormous park, even before you see the buildings dotted around it. There are mature trees, lakes, plenty of shade, and all against a backdrop of the mountains. It was easy to spend a day there and so the entrance ticket was very good value. There are maps dotted around the park, but we quickly realised we should have bought our own and went back to get one (none was offered when we bought our tickets). You can get a guidebook/ map in English. We saw a family taking a horse and cart ride around the park and would have fancied it, but we didn't see a station or any information about this anywhere.
We wandered for a couple of hours before stopping for lunch and then wandered some more afterwards but we certainly didn't see all of the museum. There are paved paths all around the museum site and also smaller tracks that take you to smaller buildings a little way from the main path. Everywhere was clean and well tended. Not all the buildings are open (you can only see the outside of some, their doors are locked), but others are fully made up inside and you can peer through doorways to see furniture, linen, equipment. There are gardens in front of many of the houses, with vegetables growing there giving the place a more 'real' feel. There are staff around tending to the grounds and we saw men cutting grass with traditional scythes.
We visited on a weekday but during summer holidays and yet there were times as we walked around that we couldn't see another soul. The park is very tranquil anyway, so it all felt very peaceful.
It really is a fantastic place to visit. I don't know of any other museums quite like this, certainly not on this scale or this attractive elsewhere in Europe.
We stopped for lunch at the restaurant called Hanul Rustic, which was just 5 minutes walk from the main entrance and near the main road to Rasinari. It was recommended in our guidebook. It was a nice place, but it would have helped if we had better German or Romanian as they didn't have the menu in English nor speak much English. However, the food was perfectly nice.
This review is the subjective opinion of a TripAdvisor member and not of TripAdvisor LLC.