I've already found the likely day trips from Helsinki, but the only day trip I've given any thought to from Stockholm is to Uppsala. Today I discovered the following on the Frommer's web site:
Some of Sweden's best-known attractions are clustered around Lake Mälaren, including the centuries-old villages and castles of Uppsala and Gripsholm that revive the pomp and glory of the 16th-century Vasa dynasty. You can spend a very busy day exploring Sigtuna, Skokloster Castle, Uppsala, and Gamla Uppsala, and stay overnight in Sigtuna or Uppsala, where there are good hotels. Another easy day trip is to Gripsholm Castle in Mariefred or Tullgarn Palace.
The boat trip from Klara Mälarstrand in Stockholm is justifiably popular. It leaves at 9:45am, goes along the beautiful waterway of Mälaren and the Fyris River to Sigtuna -- where it stops for 2 hours -- and arrives at Uppsala at 5pm. Here you can visit the cathedral and other sights, dine, and then take the 45-minute train trip back to Stockholm. Trains run daily every hour until 11pm.
That boat trip sounds really nice, so I will look into that, but it might be summer-only, so I'm not sure if it'll run in May. Still, Sigtuna and Skokloster Castle are on the route between Stockholm and Uppsala, so I could easily do all of that by train in one day. That's just something I need to figure out before I can get my rail pass.