Welcome to Stockholm Archipelago
Exactly how many islands there are is debatable, with the count ranging from 14,000 to 100,000 (the general consensus is 24,000). Whatever the number, it’s an unmissable area, unique in the world and much closer to the city than many visitors imagine (Vaxholm is less than an hour away), with regular ferry services and various tours. You can see most of the islands on day trips, but it's worth staying overnight if you have the time.
Most have good boat connections, provided you check timings in advance – although there are worse places in the world to get stranded!