I just had the experience of renting a hanbok in Jeju at Hue Culture Space (Hue Hanbok) booked through Klook and found it absolutely worth trying if you want a genuine "Korean drama film set" day. They've got heaps of hanbok styles ranging from classic to modern, including K-Drama inspired outfits, and the fabric quality and fit are lovely so they photograph beautifully. The staff will help you pick an outfit, do basic hair styling and add accessories, so you just need to turn up, choose the style you like and you've got a complete outfit ready to snap photos in.
The surrounding space is Jejumok-Gwana – a traditional Korean village area and also a film set location, so you just need to walk a few steps and you've got stacks of scenic photo spots, from brick courtyards, wooden corridors to views overlooking Jeju that are really chill. You can hire additional makeup or a photographer if you want a more polished photo set, but if not, just using your phone will give you a pretty stylish album anyway. The standard rental time is about 2 hours so I'd suggest heading there a bit early to avoid the heat, take your time getting changed, taking photos and having a wander, and just remember to wrap up on time so you don't lose any rental time.