Turistbyrå
In the Turistbyrå (“Tourist Office”) on Fyristorg, you can get a free streetmap of Uppsala, but they keep them behind the counter, so you'll have to ask for one.
Directions
From Stora Torget, walk southwest down Drottninggatan, across the bridge (Nybron), and turn right onto Fyristorg just at the Upsala Nya Tidning office. The Tourist Office is 50m up in the row of shops on the left hand side. Total distance: ~175m.
You can see the Tourist Office from the corner where the Upsala Nya Tidning office is.