Yes, the Courtyard Myeongdong is actually the Courtyard Namdaemun with an excellant view of the Namdaemun gate (and across the road from a really excellant hotteok stall at entrance 2 of Namdaemun market)
In terms of comparing Myeongdong and Gangnam. Myeongdong is a younger area and more 'everyman'. The central area where the street market and shops are gets very busy at nights and on the weekends and the surrounding areas are pretty busy as well. It's a mid range kind of place so the shops are places like Zara, H&M, and the korean equivalents and a million shops selling face masks, boob masks and all the lotions that 20 year old women use. The places to eat would be the street food, dakgalbi or my favourites myeongdong gyoza (
https://danielfooddiary.com/2015/12/31/myeongdongkyoja/) or this chicken soup place just behind the Marriot
https://goo.gl/maps/DPUyzNyERVrTWrwR9 . It's an area for younger people and not overly fancy.
Gangnam is more up market, wider streets, less people and home to all the european premium brands. It's a lot more reserved and while it is popular in the evenings its more around higher end restaurants, bars, generally fancier places. Personally I would definitely prefer to stay around Myeongdong and go to Gangnam a night or two for something specific (I'd recommend Alice and Le Chamber for cocktails) but I can see why some people would prefer to stay in Gangnam.