In colder weather it’s probably better to focus on the great cities rather than places more known for scenery and outdoor activities. If your budget is generous then my top choice would be London, Paris, and Amsterdam. You could fly into any of those and then visit the others by high-speed train. The train that connects London to Paris and Amsterdam is called the Eurostar, and the earlier you buy your tickets the cheaper they will be. Paris and Amsterdam are linked by normal high-speed trains, which are also cheapest when you buy early. Speaking of that, your dates are prime travel dates over the Christmas holidays so the airfares will be kind of expensive and they will only go up from here. In other words, buy as soon as you can.
Of the others, I’d say that Thailand would probably be your better choice. Goa is obviously famous for its beach parties, and drugs are easily available there just in case that is important, but there really isn’t much else to see or do there. Goa is a collection of beach towns, some of which are filled with raucous Westerners all winter. But once you go inland, it’s kind of falling apart, and it’s not even very “Indian” because it was run by the Portuguese until about 60 years ago.
Also, as far as I hear, the worst that ever happens is they take your stuff. So if you leave your passport and most of your money in your hotel room, and keep your phone or camera hidden most of the time, there isn’t much to lose. I’m making it sound worse than it is really. I wouldn’t hesitate to go to Rio again, but of course I’d be aware of those few situations to avoid.
If you’re a bit more on the timid side, you can always use Yelp and TripAdvisor to get good insights on places people have visited. As a disclaimer, some of the ratings may not be accurate on these sites, so make sure you go through and read some of the more recent reviews that people have written. We did this for a few of the places we visited and had no issues.