During the Staff Training Week, one of the meetings will take place directly in the Central Library on José Martího. But on the other days, you will visit several locations around Prague, thus the accommodation is up to you.
I can recommend two options which are related to the university in some way, but you can choose from many other possibilities (like other hotels, Airbnb, etc.).
Hotel Krystal
The building in which the Central Library has its seat belongs to the university, and a part of this place is also a hotel named Krystal. The advantage of this hotel is – besides the Central Library is located here – that it is on the way from the airport and near a subway station (named Nádraží Veleslavín), from which the subway line leads to the city centre. You can look at the hotel’s website here: https:/www.centrum-krystal.cz/en/.
Opitz House
The second option is another accommodation Charles University provides in the historic city centre. This hotel, named Opitz House, is a delightful historical building. In addition, there is a subway station near the hotel, from which you can get to the station near the Central Library (Nádraží Veleslavín). The Celetná street, where the hotel is located, is close to the Karolinum and the National Library. You will find more information about this hotel and booking options on the website here: https://cuni.cz/UKEN-289.html.