The only 2 rooms worth seeing in this tour, are the library and the views from the tower. The other rooms have little to offer, some just have black and white pictures of the moon, another has a few replica´s of pages of books stored in the library, and a third one some instruments (not all related to astronomy) with little explanation. In the observatory there are 2 meridian telescopes, these were used to determine the time (with a clock, which is missing) a star crosses the local meridian. They can thus only swing up and down, but not sideways. This allows one to accurately determine the position of the star and make star maps. Something similar was also done with a camera obscura and the sun, allowing for an accurate determination of midday in local time. This was used in most countries until the railway arrived, at which point it was not very practical that each town had its own time, and they introduced a standard time per country or group of countries. All this was not explained during the tour, and I only know because I am an astronomer. The telescopes themselves where not impressive to see. I doubt any serious astronomical discovery was made here, although Tycho Brahe and Kepler lived in Prague, the former did his observations in Denmark, and the latter used these observations to test mathematical models for the movement of the planets.
The library is very nice, and seems to have some interesting globes. However, one isn´t allowed to enter, or even take pictures, and only get a fairly brief glance. The view from the tower though is very nice, but then there are several other towers one can climb to get a good view over the town.
One has to take a guided tour, and there is a limit of 25 persons per tour, a tour leaving every half an hour. As a result tickets for the tours can be fully booked by noon. There is no possibility to buy online or for the next day.