If you are interested in bespoke suit, the best two places seem to be Spolverino (스포르베리노) and Lerici (레리치) for the quality. But they are not so cheap--expect to pay at least $1000 USD.
I don't really follow any Korean blogs, mostly because the biggest blog service provider Naver is shitty as hell. But the only Korean menswear blog that I follow, Andy's Room has praised these two tailors as the best in S.Korea. You can check the review for Spolverino by the forum member ho1joon's post. For Lerici suit, check out Andy's Room's this post and the other one. I cannot post images because Naver blocks it (as I stated earlier, they suck). It also seems Lerici doesn't have a website but their number is 02-549-5356.
But keep in mind that I am not sure whether you can well communicate with either tailors in English. I have no bespoke experience yet, but my impression is that the good communication between the tailor and the customer is essential to get a satisfying experience. If it seems there will be a language barrier, you might be better off with other places mentioned in SF. They would certainly be cheaper.
For bespoke shirts, the best reviewed place is Steady State and it seems they are pretty fluent in English.
For shoes, this place seems interesting. They claim to offer hand-sewn shoes with variety of customization options. They also have a shop called Diamond Walker in Singapore and you can see some of their works on their website.