South Iceland
You should plan your trip to Iceland well in advance. Since the country is small, touristy, and hotels are seldom empty, you need to secure yourself a place to stay, preferably a year before the trip. Iceland is not one of those countries that you can go to spontaneously because upon your arrival, you run the risk of not finding accommodation, especially during the season. There's, of course, an option of staying at campsites, but it's only possible in summer. And even then, living in a tent can be quite uncomfortable, to say the least, particularly during steady rains.
If you travel in summer, I suggest several route options:
1. Comfortable

Traveling by car via asphalt roads with stops at hotels.

From Keflavik Airport, head to the Gullfoss waterfall area, where I recommend staying from one to two nights at a nearby hotel. Then travel along the Ring Road to the coastal town of Vik. Plan from three to four days to explore the vicinity. Next, head to Jökulsárlón and spend two to three nights in one of the hotels near the lagoon. Finally, travel to Egilsstaðir, from where you can travel north.

In the north, stop for two or three nights at Lake Mývatn, then two-three nights in the town of Grundarfjörður.

2. Maximum:

Visiting a maximum amount of local attractions, including hard-to-reach locations via F-class dirt roads with river fords.

You will need a four-wheel-drive SUV with high ground clearance, additional equipment, fuel supplies, etc. Although the tips on how to get around the island will help you, you must be absolutely sure you have enough stamina to endure the daring adventure and your car won't break down in the middle of the trip.

From Keflavik, head to the Gullfoss waterfall area for one or two nights, then take road 35 to the Kerlingarfjöll Mountain Resort for one night. Stay three to five nights at Hrauneyjar Highland Center Hotel and make radial trips to nearby photo locations, including the Veiðivötn Lakes, where I recommend lodging for one night in the cabin. Take the scenic road 208 and head to the town of Vik for three-four days. Spend the next two to three days of your trip exploring the Jökulsarlon lagoon while lodging at one of the nearest hotels. In the town of Egilsstadir, I recommend spending a couple of days and then exploring the northern part of the island.
3. Budget

Driving an SUV and lodging at campsites.

You can bypass hotels entirely and stay at local campsites, such as those found in the Landmannalaugar and Hveravellir areas, which you can only reach by driving an SUV, those near the Svartifoss waterfalls and in front of the Skógafoss waterfall, in the town of Vik. In the north of Iceland, there's a large campsite near Lake Mývatn.

Typically, campsites have a paid shower, kitchen, and toilet. Unfortunately, there's no electricity.

Alternatively, you can travel in an RV.
If you are traveling to Iceland in winter:
During winter, the roads of the central part of the island are closed. You can only travel by taking the Ring Road and adjacent asphalt roads. Since you won't be able to reach some of the locations, it makes sense to travel around the entire island via the Ring Road and visit both the south and north of the island.

If you move from Keflavik from west to east, I recommend making the first stop for one night at one of the hotels near Gullfoss to photograph the waterfall. Then move to Vic, and spend two-four nights there. Go to Jökulsárlón for two to three days. Take pictures of the glacier and Stokksnes. Then move to North Iceland.