It's not a bad month but don't expect to go to the beach or anything alike. All pubs and kiosque are closed.
Depends on what you are looking for. One thing you have to know is that we are out of touristic period so the historical sites are open only from 9 to 14. If you look for those things, the best is the Peloponese region in my opinion: A lot to see, nice cities, great mountains (I love Sparta and the old city of Mystra). The region of Thessaloniki is great as well, fewer sites but they are nice as well. However if you want a great city to live in, with parties and so on, I'd pick Thessaloniki. There is the same in Athens but I don't really like our capital tbh.
To avoid: Epirus and Ioannina. It's a wonderful city and a great region but if you don't want to be stuck in the middle of the mountain with a block of a ice on one side, a ravine on the other and 20 cm of snow, it's not the good plan :D (well, it happens during winter so you have to pay attention in those areas)