You didn't say where you would be going in Greece: mainland, islands or a combination of both. Depending on what country you are coming from and the weather there in January Greece may have better or worse weather than where you live. On the plus side is that there will be hardly any tourists. If you are prepared for Greece's weather that time of year it may be a decent time to visit since it's way off-season, less tourists and excellent prices, however many businesses will be shut down but enough open for locals to eat out and everyday shopping so if you are not fussy you'll have enough places to eat and shop.