Kapuzinerberg -- This forested area on the right bank of the Salzach River rises more than 610m (2,001 ft.) above the city and is today a landscaped park. To get here, cross the Staatsbrücke spanning the Salzach to the right bank, continue walking for 2 minutes until you come to Steingasse, and cut right; after exploring Steingasse, walk through the Steintor, then climb an adjoining stone stairway, and follow the signs to Kapuzinerberg. You can also take bus no. 2, 5, 6, 15, 27, 29, 51, or 55.
A Capuchin friary was built here at the very end of the 16th century, constructed inside an old medieval fortification. On the south side of the hill are Steingasse, a pretty street from medieval times, and the Steintor, which was once a gate in the walls of Salzburg. From vantage points on the Kapuzinerberg, you can see into Bavaria, in Germany.
Mönchsberg -- West of the Hohensalzburg Fortress, this heavily forested ridge extends for some 2km (1 1/2 miles) above the Old Town and has fortifications dating from the 15th century. From several vantage points, including the Mönchsberg Terrace just in front of the Grand Café Winkler, you can see Salzburg.
You can get up here by taking the express elevators leaving from Gstättengasse 13 (tel. 0662/44806285). The elevators leave daily from 9am to 1am. Round-trip fare is 2.90€ ($4.70) for adults and 1.60€ ($2.60) for children 6 to 15; it's free for children 5 and under.