Best info I could find online is a Icelandic WhiteWater custom google map Icelandic WhiteWater - Google My Maps. From what I could tell, and perhaps influenced by the high spring melt water encountered, the creator was not loose with class grading. So even something labeled class ii on that site will likely be a handful in a packraft.
Details for a couple of things run and a couple of further details on things scouted but not run, to scratch the surface:
Hvita river from below Gullfoss falls to highway 30 bridge. Put-in is river right, not left as mentioned on the IW page. About a mile south of the falls parking lot turn east off highway 35 towards Hotel Gulfoss. A large path within sight of the hotel will be on the left. Walk that path and just before this path goes up a steep hill turn right onto an abandoned trail (not noticeable at first). When in sight of river go straight down to the right of the shrubs. There might be a footprint or two from a rare recent paddler. It is a steep but not difficult walk down. Should come to the river at a boulder garden, walk upstream a bit to wherever looks good to start. Total walk about 20 minutes. River fortunately can be whatever one wants to make out of it and most rapids can be scouted, if desired. There are some wicked looking large holes in places, but they can be fairly easily avoided, letting one keep it to class ii/iii without any portaging or iv if want to partake in all of the festivities. Just about the perfect packrafting run, plenty of excitement. Easy takeout 100-200 yards before the highway 30 bridge river right, there is a place to skirt around the barbed fence at the bridge. The IW page says takeout past the bridge but I didn’t scout that. The next takeout is the highway 519 bridge, appears this lower section becomes bigger, flatter, and more susceptible to headwinds. Time to run the upper segment is about an hour and a half with a little bit of stopping/scouting/enjoying.
Olfusa river in Selfoss. There is a half mile play spot in town near the bridge. Put-in river left, walk on pathway upstream until come to a little used gravel road along the river. Take this about a third of a mile, put in around where it ends. Takeout river right just after the bridge and bend. Class ii.
Jokulsarlon glacier lagoon. Packraft comes in handy to paddle around good sized icebergs and get away from the “crowds”. Park in one of the small lots a few hundred yards west of the bridge and large parking lot for paddling.
Grimsa near Egilsstadir. Put-in is river right at the dam, off highway 1, there is a steep ravine that goes to a tributary right below the dam. There may be another way not seen on this journey. There is no way to put-in river left (canyon). Water seemed to be running high over the dam from spring melt on planned day and was making a maelstrom into the opposing canyon wall that did not look like good news for an idiot in a packraft. Take out is river right at farm Asgardur or river left at highway 931 bridge.
Fjardara near Seydisfjordur. Put-in for the lower section is below the last waterfalls river right, one of the more scenic places for a put-in. There is a walking path from the center of town that goes along the south bank of the creek for awhile, then turns left onto roads at outskirts of town, then goes near the cliff past awesome waterfalls until it returns to the creek at waterfalls and a house/building with a footbridge. It is marked with stakes. Nice creek ii- run takes you right back to town, take out river right at the park after the town bridge. Apparently local kayakers run some of the waterfalls higher up. None seen that didn’t look insane although any at the very high altitudes were still under snow at time of writing.
Godafoss Falls. Judging from youtube videos and scattered intel, the river right falls could be doable in a packraft with normal water levels. Put-in is just a few feet up from the falls, river right, so not much time to think about it. The line is as right as one can get to be spit out nicely at the bottom. Takeout is river right immediately after the drop. At spring melt high flows as observed, the pool at the bottom is washed out, probably still ok, but the high water removes any safety factor of taking out for a swimmer, and missing the takeout at any water level results in a really bad day as one would then go through the next falls, Geitafoss, which at high water looked like sure recirculating death.
Godafoss, non falls option. Believe this might only be a high water level possibility, unsure. Put-in is river right upstream from Godafoss Falls, just past the powerlines gives just enough space to do the required paddling to get to river left. There is a channel to the left literally just feet upstream of the left Godafoss falls, so it is pretty critical to be all the way river left to make that turn. Another option would be to just put-in from the falls parking lot at this channel, but that wouldn’t be nearly as much fun as freaking out tourists hanging out that might think one is about to commit suicide by 5 pound raft. This channel begins with a decent class iii drop on its own. LPT secure prescription sunglasses before being upside down in a packraft going through this, if anybody finds them let me know . If takeout near the cell/radio tower it can be kept to class iii. It becomes iv just before the bridge and supposedly after the bridge gets quite sporting. The IW page has takeout river right after rejoining the main river.
General: This is packrafting mecca. All the water types of Alaska, just without any wood to ruin a day. There are potential runs just about everywhere for all skill levels. One could just start out on the tundra as far as desired and raft back to a car or make an epic multi-day journey. Iceland rivers can be part of private property (believe to fish one needs owner’s permission), but overland wandering and accessing rivers seems to be okay for the most part. Finding a turnout or level shoulder on the roads anywhere that is not a normal tourist spot to park a car can occasionally be difficult. Hitchhiking, if necessary to get from takeout to put-in, seems to be a fairly common mode of transport, although one is generally at the mercy of other tourists who likely have a lot of gear packed in a small rental.