Dayton is still there.
As with pretty much all the tailors, they outsource their work. The actual tailors CAN do what you ask for, you just need to know to ask for it. If you don't specify the quality and details to the tee, you will get a substandard product.
First of all, forget the expensive import fabrics. The import taxes and tariffs make them prohibitively expensive. Either bring your own, or use the local Samsung fabric. Make sure to specify you want the "top quality" 100% wool from Samsung. It is actually pretty good, I would compare it to the usual Vitali Barberis Canonico Perennials and such. VBC is usually twice the price for a suit in Seoul. If not, run away, you are getting a Chinese ripoff (not unheard of, especially in Itaewon).
Also, don't be fooled by the business card roulette. Asian tailors love to collect pictures and business cards from influential people. Sun Custom Tailor has pics of Barack Obama and GW Bush the second, and nobody seriously thinks they tailor for them.
In Seoul, there are a few top-of-the-line tailors, obviously not in Itaewon. But then you must invest 1500+ USD per suit.
The "benefit" of Itaewon is that the sales people speak OK English. BNTailor, Spolverino and the very good "local" ones, English is a hit/miss.
The cheaper ones work as long as you know what you want and have the time to insist on them getting it right.
My first blazer project took about 3 weeks and 6 fittings to get it cut just right. Tailors(I mean the people who actually do the job) there are often too sloppy with details, they tend to cut the coats very boxy (Which makes a fatass like me look even worse). Also look for very low armholes, and with the first basted fitting you need to know if they have the front/back balance off, which will make for a godawful looking suit and cannot be altered later. (Somewhere this is called "open" or "closed" quarters, where the bottom front of the jacket either opens way too wide of is completely closed making it look too big).
So, if going for a first comission, be prepared to know what you want, don't settle, and don't go for a place that says they can do it in 2-3 days.
My current recommendation is Savile Row, end of Itaewon-ro, close to Noksapyeong and the army base. He has been there since the 70's, speaks good english, and they got most things right the first time. He also seems honest and so far hasn't complained at all about my endless requests for modifications.
General things to look for:
Full canvassed construction. Usually the norm, accept nothing else. If they offer half-canvas or fused, walk no, run, away.
100% actual pure non-synthetic top quality pro cool hyper amazing wool. Some places (such as Dayton in my recent experience) they offer this as like second of third option. The first ones they want to offer way too often are "wool and silk" or "wool and cashmere", but if you pull out a lighter and explain you know how to do a lighter test, they will pull back and offer the best quality wool, which is almost without an expection made by Samsung. Its good, it gets ALOT better after you wear it for a while. Italians and especially the Brits process the fabrics better so they have a softer hand right away.
Working cuff buttons. Unless this is specified, they often cut the sleeve without any opening for the cuff, makes it look silly.
Horn buttons. They often use plastic unless specified, usually a no-extra-cost option.
High armholes. This needs some expertise from your behalf too, but the "standard cut" often is very low.
Shoulder fit. Koreans tend to prefer suits that emphasize their shoulders. Many western people look like they took the time machine back to 1980's and their Armani powersuits. Ask for little to very little shoulder padding. Their "normal" tends to be "alot".
Shoulder height. Most people have one shoulder that sits lower than the other. Ask them to check and cut to suit. If this is incorrect, the lapel won't curve naturally over the chest, when the coat is buttoned.
If you want to have fun, ask for hand-set collar and an L'Asola Lucida buttonhole in the lapel. See what they say
Disclaimer: I am not a tailor, my terms are inaccurate and maybe incorrect, but I've got both good and bad experiences with tailors around Asia. Even though I've only lived in Seoul for some months now, I've talked to many of the suit sellers in Itaewon and elsewhere, so I sort of have an idea who are there only to take money from the passers by, and who care about long-term business relationships.