Nektarios's place is great! It's as close to the National Archaeological Museum as you can get, there are several grocery stores in the immediate area within a 10 minute walk (Several Bazaar markets and an OK Market which is open on Sundays and later hours), some great restaurants are in the neighborhood too. I really enjoyed Saligaros and I Kriti... There is a coin laundry (Bougada) about a 10 minute walk away as well. As far as proximity to the main historical sites, they can be reached with about a 25-30 minute walk, or less if you take the Metro.
As far as the apartment itself, it has everything that you could want. I stayed there for a month, and was perfectly comfortable during my time there. The kitchen has pretty much everything you need to cook meals, the bathroom is fairly spacious, the bed and couch were both fine as well. The hot water and air conditioning were both stellar. The internet connection is DSL that usually got me about 15MB download, which was fine for my needs. I only had one very brief internet outage, but that was on a day when North Athens was devastated by a wildfire, so the outage is completely understandable given the situation.
Finally, Nektarios is a super, super nice person! He had a family situation that required a lot of his time during my stay, but he was always very responsive, and seemed to really regret not being able to spend time with me to chat and fill me in on the details of Athens. Personally, that's something that I always look for in a host, a willingness to spend time with a guest, but also a willingness to leave them be if that's their preference.
All in all, I had a wonderful stay, and I recommend Nektarios's apartment without reservation!