Begin at Staroměstské náměstí (Old Town Square). It's the heart of everything. You've got the Astronomical Clock on the Town Hall — watch it if you arrive on the hour, but don't feel obligated. There's also St. Nicholas Church on the north side, and the square itself is ringed with cafes and shops.
Grab a coffee here if you want. The pace is already yours to set. From the southeast corner of the square, you'll head toward Nerudova Street. Don't take the obvious main streets yet — instead, find the narrow lane called Maiselova. It's quieter and gets you into the character of Old Town quickly.