We've stayed in all three for staycations while living in Seoul, during COVID times. Although it was pre-delta wave, and things were a bit more relaxed.

If you have to choose just one I'd pick Park Hyatt. By far the best overall "upscale" feel, it's kind of fun to be near COEX in my opinion because there's so much shopping and so on. If it's just the two of you the COVID restrictions wouldn't apply since the limit is meetups with 2 people at night (if you're vaccinated then you can meet up to 4, however, right now, though you have to make sure you can verify this electronically). We did a weekend FHR staycation and we got upgraded to a higher floor with a spectacular view even as an Explorist. I think there's a better chance of an upgrade than you think because due to COVID there aren't many foreign tourists so you can often get something nice even on weekends right now.

However if you plan to do room service I'd say the Grand Hyatt has the best room service kitchen. The food was astoundingly good for some reason, at least the dishes we tried there. Park Hyatt has a much better breakfast downstairs than the Grand Hyatt buffet breakfast, though. I have to say the rooftop restaurant in the PH didn't wow me that much with the food but the view is amazing. There are other restaurants in the hotel we never tried however.

Of the three for me the Andaz was the least great in terms of the room itself. The hotel has a colder feel and the rooms for me are less luxurious, we had a balcony suite but it was kind of small and on a lower floor (perhaps for safety?) There's a fun little mini-mall in the basement with some food options, though, and it is right in Apgujeong with some very high-end dining and retail all around that area.