South Korea has a lot to see outside of Seoul, but I had too many planning on my hands, so I through them in the air and instead of reading the entire guidebook and try to decide which areas are worth trying to go to, and worrying about transportation, which would have been non trivial in the rural areas (I could have driven the many km, but I wasn't really keen on it, I hate driving distances for hours), I cheated and booked an eastern korea tour with hanatours.

This was a bit of a gamble as we like flexibility and going where we want when we want. That's obviously impossible with a packaged tour, but I figured in this case it would make sense for 4 days, so I found and went with HanaTour/Korea Package Tour. Turned out that while we did indeed lose flexibility, it was about as good as it could have been, considering. The bus was a luxury coach with nice seats and power (so I could work on my laptop and do trip planning/picture processing during the 1-4H drives between locations).
While I'm sure we could have seen more on our own, it would have taken considerable effort, not counting dealing with the car, parking, hotels, restaurants, which was all done for us here. I'm not sure what we missed by being in the bus, but it felt like they picked a decent list of things to see, and while the days were a bit shorter than they would have been for us due to other more pampered people in the bus who don't want long days and aren't as active as us, I think it worked out well enough.

We had a nice bus, quite comfortable and with power for our laptops during the longish rides between locations:

nice bus

The first day we had a 4H drive to the South towards Jinju to see an old fortress that was used to fight Japanese invasions (even if they lost in the end):

the general who successfully defended the city until he died

Next, we went to Busan, the 2nd biggest city in South Korea. It's known for ports, marine trade, beaches, and big buildings. They also have the APEC house, used for Asia trade agreement talks.

buildings where you can open windows, nice (and unusual)

We had dinner at Shinsegae, the biggest department store in the world:

they had a very nice collection of French wines, some priced up to $4000

We ate those puffer fish, poor things

the roof had a viewing area/dinosaur park for kids

At night, I went to see the nearby night market and took some random pictures:

the poor baby octopus didn't know that they could escape

I'm not sure I'd want to eat this

The next morning we went from Busan to Ulsan to visit Ulgi Park, a seaside park with exercising machines and a big dragon slide:

The biggest car manufacturing plant in the world (Kia) was there with lots of cars ready to ship on boats:

Then, a lunch stop, before heading to Gyeongju, starting with Bulguksa temple:

nice guardian statues, they reminded me of the similar ones in Nara

dragonfish

We got to learn about the Silla Kingdom, they reigned in the area between around years 58BC to 935AD and had a very good civilization going on there. Interestingly they burried their kings under big hills made out of stones (now seen as inverted craters filled with grass):

location of tombs

the tombs now look like big mounds

one was escavated to show what it looks inside

early game of go

what things used to look like

the oldest bell in Korea, dating 771

We finished by spending the night in the city, eating at a nice buffet restaurant:

The 3rd day, after a nice buffet breakfast at the Hilton, we went to the historic village of Korea at Hahoe:

wishing tree

Next, we went to Wonju's Hanji Museum, where we learned how they make paper the old fashioned way, and we got to build a little box with their colored paper:

Dinner, was a nice BBQ restaurant, where we had to take off our shoes again:

And we arrived at Alpensia for our night, the future site of the 2018 winter olympics:

ski jump ramps

tame bunnies running around our hotel

The next morning, we went to Jumunjin Fish Market. It was definitely interesting to see, but we were a bit heartbroken to see all those poor octopuses that had been caught and were on their way to dinner plates. If you wonder why I care more about octopuses and cuttlefish, it's because having seen them on several dives, they are highly intelligent and communicative. Think of it as eating a house cat, except an animal that is actually much smarter than a house cat. Just what they're able to do with color patterns on their body, and even change their body shape and texture, is quite impressive. That's why I care more about them than let's say a crab or lobster or run of the mill fish, none of which are smart.
Anyway, some pictures:

red octopus

black octopus, as big as the ones we found in the ocean on our own

squid

a big one trying to escape

lots of red crab

ray

Next, we drove to the Seoraksan National Park and hiked down a nice trail:

fish heads, fish heads, happy merry fish heads...

last big lunch, way too much food again

And after that, we headed back to Seoul, to be dropped at Lotte Hotel. From there, we did a quick tour of Seoul on our own before the end of the day.
As for Hanatours who organized and sold us this package, I think they did a very decent job to try and please everyone considering the range of customers from pampered and not willing to walk/see much, to super active like us. Jason, our guide, also did a very good job. All in all, it was a good choice to go that route instead of doing all the work to try and organize that ourselves, not counting transportation, harder in those towns.