Konstantinos was super flexible with check-in / check-out. We only stayed there one night, as we were getting in from Piraeus late at night (around midnight) and leaving from ATH early the next day. It was a perfect spot to post up for a night. It is located right in between Monastiraki and Syntagma Metro stations (5-10 min walking from either).
The apartment itself is simple and clean - all we needed for a quick pit-stop before a long day of international travel. The instant coffee provided was a nice plus. This no-frills apartment had all the basics. Note that the building appeared to still be under development - probably not ideal for young kids or elderly travelers. However, as a young couple we had no problems whatsoever.