Everything inside the old moat is a ten-minute walk, so the choice is really between the noise of the two squares, the quiet of the university streets, and a cheaper bed a tram ride out by the station.
Horní and Dolní náměstí — the two squares
You wake up next to the Trinity Column and the town hall, with most of the restaurants and the tram stops at the edge of the square. Loud on Friday and Saturday when the student bars fill; quiet mid-week.
Around the university — Křížkovského and Univerzitní
The lanes between the cathedral and the squares: faculty buildings, canteens and the Archdiocesan Museum. Five minutes from everything without the square-side noise, and where the student prices are.
Hodolany and the main station
Fifteen minutes from the centre by tram, across the river and the rail yards. Nothing to look at, but the cheapest beds in the city and the obvious base if you are arriving or leaving late by train.
Practical: buy the tram ticket before you board
A basic DPMO ticket is 25 Kč from a machine, the app or by SMS and covers 40 minutes on weekdays, 60 at weekends. Bought from the driver the same ride costs 40 Kč. A 24-hour ticket is 90 Kč.