Are things open in January in Dubrovnik? Is the weather rainy?
Can't speak to Dubrovnik, although the cruise ship season would tell you a lot -if they stop coming, stores will close up. But in Rovinj, a delightful town in N. Croatia, the season ends more or less on Nov. 1st, All Saints Sunday, a big family celebration of the dead, and by November most restaurants have closed and taken away their summer tables and chairs and laid off the staff. Annual vacation (godisni odmor) signs appear in store and restaurant windows, and the place settles into another rhythm. But there is a move to winter tourism, and New Year's Eve parties are advertised by major hotels hoping for big bar bills. You can find out from the Dubrovnik TZ or Turisticka Zajednica office online what is on, if anything, at that time of year. Seasonal workers will have returned to towns and villages across Croatia to last until spring. Squares and side streets will be empty except for locals, which can be a very good thing. If a few facilities you like are open, even with the cold rain and storms that pummel the Adriatic in winter, there are still many sunny days to enjoy, mandarine oranges to eat,and a Dubrovnik without cruise ship passengers would be a very pleasant visit. Days will be short, so bring lots to read or find an internet connection. Your choice of evening eating out will be limited compared to summer -a self-catering apartment might be wise, and cook your own meals. But you are likely to meet those people who were too busy and/or touristed out in summer to talk to you, and may make some fine new Croatian friends. Bring a warm waterproof coat and a sweater, a solid umbrella and non-slip waterproof shoes, and enjoy another Croatia from the 40C summer version. Watch out for slippery stones!