This old picturesque town is well preserved and worth a visit, and on the mountain high above the town you'll find the fort Castel St John (Tvrđava Sveti Ivan) situated on the cliffs, overlooking the bay. It'll take you about 45 minutes to walk to the top on the old stone stairs. It's said to be about 1350 steps, but we didn't count them... Just as we reached the top it started to rain, but we could still admire the magnificent view before returning to sea level, a bit wetter ;-)
Just outside Perast you'll see the small island Gospa od Škrpjela (Our Lady of the Rocks) in the bay. It's built on a reef and there has been a temple here for more than 500 years. We took a boat taxi from Perast to the islet, mostly for the nice views around the bay.