I say go to Thailand. You're going to have to rip that band-aid off eventually, and the earlier in your 20s you do it the better - there's a reason it's become the de facto tourist destination for people in their 20s. Head to Koh Tao and get your scuba diving certification, then spend a few days on a liveaboard if you can afford it. Go to a full moon party on Koh Phangan. Party it up in Bangkok with all its crazy weirdness. Head North if you want to get in some jungle trekking. Buy a couple of new suits and a bunch of shirts for your new job on your way home.
If you're not so interested in Asia, head to Eastern Europe for a while. Do a couple of quick stops in Amsterdam and Belgium (only if you like beer), spend a few days in Berlin, have a gander at Prague and Krakow. The more time you spend in Eastern Europe the cheaper your trip will be.
You might find Nicaragua/Costa Rica/Panama a good trip too, particularly if you like nature and volcanoes.
Truthfully, 3 weeks isn't that long, so you probably want to minimize travel once you get to your destination.
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