Hiking -- Shoddy trail maps are available for 300kr ($4.80/£2.40) from the visitor centers, but trails are well-marked and you can probably just memorize or jot down your route from signboards. For longer hikes, serious maps should be available at the information center.
Apart from the historical sites, and the north-south trails connecting the sites to the information center, all trails extend east into the Þingvallahraun lava field. All the field's lava flowed about 9,000 years ago from Skjaldbreiður (Shield Volcano), a perfectly rounded, squat cone visible to the north once you're out in the field. Named for its shape, Skjaldbreiður then lent its name (in translation) to all other shield volcanoes, just as Geysir lent its name to all geysers.
As is clear from the map, virtually all the trails leaving from the western edge of the park converge halfway across the valley at the ruins of Skógarkot, a sheep farm abandoned since the 1930s. Each trail takes about 30 to 40 minutes. Skógarkot is now just a pleasant, grassy spot on a high point in the field, with a few stone foundations. Further east lies Þórhallastaðir, another farm ruin, but Skógarkot is more picturesque and enough to satisfy most day walkers. It's also an ideal picnic spot, with a great view over the lake to Hengill and the Nesjavellir geothermal power plant.
A recommended loop itinerary starts and ends at the information center. If you have 3 hours, head south along the fault to the historical sites, then take the trail east from the church to Skógarkot, cutting directly back to the information center. With only two hours to spare, park near the historical sites and squeeze in a hike to Skógarkot and back. If you have just 1 hour, stick to the historical sites and venture north along the fault. Remember that you can time your trip to take advantage of the free 1-hour guided tours of the historical sites, leaving from Þingvallakirkja (Þingvellir Church) at 10am and 3pm weekdays, June through August. Serious hikers can follow a trail all the way to the eastern edge of the rift -- near to where Route 36 climbs the eastern rift wall at Hrafnagjá -- but it's too long for a return trip in 1 day, so you'd want to arrange a ride one way.
Forty percent of all Icelandic flora can be found in Þingvellir, but nothing is taller than a dwarf birch. It's especially pretty in fall. As you walk through the valley, be careful not to step into the many fissures along the trail, and keep a close eye on children.
Scuba Diving -- Diving in Þingvallavatn has taken off recently. Dives focus on dramatic fissures on the lake bottom, up to 40m (131 ft.) below the surface. Þingvallavatn is not recommended for beginners, given the cold temperatures and currents inside the fissures. Dives must be reserved in advanced.
Near the Golden Circle
River Rafting -- The Hvitá is Iceland's most popular river for white water rafting, with fabulous scenery and easy to medium-difficulty rapids that don't require previous experience. Every afternoon from June through August, the recommended tour operator Arctic Adventures (Laugavegur 11; tel. 562-7000; www.adventures.is), sets out from its Drumbó base camp, signposted from Rte. 35 about 10 minutes' drive south of Geysir. The three-hour tour -- with timeouts for cocoa and cliff jumping -- runs 6,590kr ($105/£53) per person, or 9,590kr ($153/£77) with pickup/dropoff in Reykjavík (minimum age 12). For 7,990kr($128/£64) per person (9,990kr/$158/£79) from Reykjavík), more daring paddlers can tackle the river in two-person inflatable canoes.
Note: This information was accurate when it was published, but can change without notice. Please be sure to confirm all rates and details directly with the companies in question before planning your trip.