The lagoon boat trips are excellent, but you can get almost as close to those cool-blue masterpieces by walking along the shore, and you can taste ancient ice by hauling it out of the shallows. On the Ring Road west of the car park, there are designated parking areas where you can walk over the mounds to visit the lake at less-touristed stretches of shoreline.
The closest accommodation is at the hamlet of Hali, 13km east (no camping at Hali; the next campground east of Jökulsárlón is in Höfn).
Accommodation along this stretch of the Ring Road is in hot demand; book early. (Note that there is no need to book campsites.)
There is a small cafe and souvenir store in the eastern car park, and a couple of toilets, but the dated facilities are woefully inadequate for the number of visitors. There are hopes for new facilities now that the area is part of the national park, but this may take time. In the meantime, you can enjoy good snacks from food trucks.
This is a true Iceland highlight, so countless day tours take in Jökulsárlón. Trying to do a trip from Reykjavík to the lagoon and back to the capital in one day is not recommended (it's 375km, or about a 4½-hour drive each way).
In summer, the lagoon is a hub for boat tours and some kayaking. In winter, the car park swells with super-Jeeps ready to cart travellers to ice caves. This is generally the location with easiest access to some of the most-visited caves, so tour operators meet tour participants here. The tours are run by companies that have summer bases elsewhere along the stretch between Skaftafell and Höfn, including Arctic Adventures, IceGuide, Glacier Journey and Ice Explorers.