Which hotel is good for stay in korea with a baby? Any recommendation?

Not sure which area are you asking for, you can consider Metro Hotel in Myeongdong. They offer family friendly facilities such as child equipment rental (Strollers, Bouncer, Baby crib, Waterproof mattress cover for bed wetting), Child safety kits (outlet covers, toilet trainer seat, night light, baby chair, booster) and some other stuff. You can refer to this link for more information: https://www.metrohotel.co.kr:11031/specialoffer/family.asp

Which part of Korea will you be holidaying at? The usual big names in Seoul are usually very baby friendly -- JW Marriott, ibis, Hilton etc. I've also heard great things about Sheraton D Cube Hotel. These hotels are also quite central and near lots of attractions :)