St. Petersburg is known to be a great city for walking, and this is indeed true, provided the weather holds up and it isn't getting dark at four in the afternoon. Nevsky Prospect is the main drag, and most places in the center are only a half-hour's stroll away.
Not far from the top end of Nevsky you can explore several famous squares, including: Dvortsovaya Ploshchad (Palace Square), flanked by the Winter Palace, which houses the Hermitage Museum; Dekabristov Ploshchad (Decembrist Square), where that popular Petersburg landmark the Bronze Horseman rears its famous head; and don't forget glorious St. Isaac's Square, home to St. Isaac's Cathedral and, of course, the St. Petersburg Times office.
Letny Sad (the Summer Gardens) is perhaps the nicest of the garden and park areas, originally designed as a quiet place of contemplation and meditation. Mars Field and the Mikhail Gardens, near the Russian Museum and the looming onion domes of the Church of the Resurrection, are similarly attractive. There is also Tavrichesky Sad, near Chernashevskaya metro station, which is well worth exploring.
The Strelka, at the eastern end of Vasilevsky Island, is an interesting place to wander and boasts one of the better views of the Peter and Paul Fortress -- located across the water on Zayachy Island, also a nice walking area with parks and a zoo nearby.
Further away from the city are several nice old tsarist palaces, surrounded by lavish gardens -- the most popular being located at Petrodvorets, Pushkin, and Pavlovsk. Good places for picnics and favorite weekend getaways for locals and tourists alike.