Spent about a week at Lexville. Was in Seoul for a conference, so didn't do much sight seeing. It's about a 45 minute subway from most of the major palaces, museums, Namsan Tower, etc. However, it's super close to the Gangnam district, COEX Mall, Lotte World, etc. There's a ton of great restaurants literally around the corner in the Jamsil neighborhood. If you want to cook in, there kitchenette includes some basic stuff (small pot, non-stick frying pan, spatula, electric rice cooker, cutting board, knife, flatware, etc.). I couldn't find a grocery store nearby, but the convenience store on the first floor has some basics (eggs, bread, etc.).
It's also surprisingly quiet, given the busy neighborhood. The windows keep out pretty much all the street noise.