I’d really try to get another week. Three weeks is just enough time to get comfortable in a place.
Ethiopia is top of my “next destinations” list. I’m a “go where the wind takes me” type, so I’d probably just fly in to Addis and go from there.
Other options would be visiting friends in Mali and then wandering out to Senegal, or going to China to see my old students and make it to Xinjiang.
Great choice!
I’m with simsimian and MacCat. In 2 weeks, I could do a lot in Costa Rica with 3 grand.
I had a great week at Buddy Dive about 5 or 6 years ago. It’s a good choice.
My first reaction, though was “I’d like to go back to Fiji.”
Costa Rica is also a good choice. All depends on what “fun” means to you!
I wouldn’t turn down a return trip, either…
-D/a
I haven’t been in many years, but when I do go again, I would love to do at least a couple of days here
For me, it’d be Thailand. Or Istanbul. If you’re thinking Europe, there’s no point in getting unlimited Eurail if you’re only going for 2 weeks, though, just pick one big or two small countries and stick to that. Of course, IMHO, Prague is the most beautiful city of Europe, so if you haven’t been there yet, go there.
I’d want to go everywhere, but for some reason Italy appeals to me right now. Someplace with hills, not too hot, some breeze and a mellow sun. Ruins and/or water is nice but not necessary. Just somewhere out in the country.
Or somewhere in the Euskadi where there’s no turmoil going on.
Or Montenegro, but I want it all to myself…no tourists! 
I’d book two weeks at an all-inclusive resort in Jamaica, then just lay around eating, drinking, smoking cigars, and ogling the young ladies in their swimsuits (or in no swimsuits, depending on the resort).
The British Isles. I’d plan my itinerary but it would get shot all to hell because I’d want to see everything of interest at each place. In fact, I probably couldn’t bear to leave without seeing everything I wanted to see, so I might end up having to live there for awhile.
I’m convinced! So is one of my coworkers. If and when I/she/we go to Costa Rica, that is definitely a destination!
Do the travel expenses come out of the $3000?
Italy. Two weeks is enough time to hit Venice, Florence and Rome. Venice really is as beautiful as you think it’s going to be. Florence is a bit dirty but the art treasures are amazing. I’ll never forget a twilight spent listening to live music next to the Uffizi. Rome is my other favorite city after New York. The fabulous pizza by the etto, the Vatican museum, Trevi fountain at night, Julius Caesar’s grave – you’ve got to see it.
Then again I spent two weeks in Costa Rica on my honeymoon and loved it madly. Go to Tabacon hot springs and watch the monkeys in the trees at Manual Antonio national park. Or just sit back and watch the hummingbirds everywhere. Monteverde cloud forest is also amazing. We took a night tour and saw wild toucans.
You see, that’s my problem. I pretty much have all that and have been trying to decide on where to go this year, but haven’t pulled the trigger. I’m mainly focused on Ireland but the Greek Isles keep calling my name, as well.
Chile. Go at a time when I can check out the aurora australis as well.
What is so crazy about Thailand vs other East/Southeast Asian countries? I’ve never been to any of them, so I’d think any would be a headtrip for me. Other than the jokes about the hookers in Thailand, I don’t know anything that makes it any stranger.
My safe pick would be England just so I could watch lots of soccer on the weekends, and take some short trips to Paris, Brussels, and Amsterdam. I don’t know off hand if $3k would be enough money, but if so, it’d be a coin-flip between Patagonia and Tanzania (to climb Mt. Kilimanjaro).
Any island in the South Pacific or Caribbean would be nice, but I think I’d get bored after a couple weeks, even if I were island hopping.
I don’t think Thailand is any crazier than other East/Southeast Asian counties. I just think it can be more “accessible” to a first time traveler.
The government is pretty easy to deal with as a traveler, you don’t need a preapproved visa. Officials aren’t going to hold you up or charge “extra” fees.
The people are friendly and even the cons they run are basically harmless and somewhat entertaining.
If you really get into the adventure, it can be extremely cheap, but at the same time if you are overwhelmed, you can get yourself to a nice western hotel room with western toilets and a breakfast buffet for $40.
No landmines
I guess the point is that you can kind of pick and choose what level of adventure you want. Be a backpacker for a few days, eating grasshoppers and catching rides on the back of a truck, or a big spender, laying on the white sand beaches drinking Mai Tais and eating lobster.
I would spend as little as possible getting to Canada, and stay there.
Seriously, I would go somewhere warm and beachy, get a hotel room with a private beach, and eat some great food. I don’t like amusement parks or shopping. Maybe Mexico along the gulf, I really like authentic Mexican food and margaritas. Or if I was feeling particularly rambunctious, I might book a flight to Cuba through Canada. Cuban cuisine looks good.
Costa Rica is a good choice (and flights seem cheap to CR right now), but I came in to suggest Peru. An unplanned backpack vacation in Peru can be had for less then $3K. Machu Picchu, Cuzco, Arequipa, Lake Titicaca…all good places to visit.
Frankly they all sound fairly fun. Oddly enough, I have a passport, and time on my hands but alas no money. 
If I was going solo [you didn’t say if mrAru would also have $3k or if we had to split the $3k, or if I had to do this all alone:D]
I would say if I was going to go it alone, My $3k and I would make plane reservations to Iceland, where I would check into a nice midrange hotel and do some sightseeing. I would definitely hit that hot spring lagoon for some quality soaking time, hit up a spa for some massage and mudbath type wrap treatment. Maybe a nice session at a beauty salon for a nice haircut, get the legs waxed again and a professional dye job - maybe purple again. If I could hit it at the time of the EVE Online con, that would be fantastic!
Alternately, London. St John’s hotel and restaurant for the digs, a nice 3 day weekend of relaxing and eating. I would set up a private dinner there for my EVE online buddies, and treat myself to a spa day beforehand with the aforementioned haircut, dye and massage type stuff.
2-week road trip, New Zealand south island.