I have pretty much this situation coming up this fall. My plans are to take a tour in Scotland. I’ve never been farther north in the UK than Inverness, and that was over 20 years ago, so I’m thinking of spending most of my time up in the far northwest.
Right now? I would go someplace warm. Ideally, I would go to a place where I could learn something. There is a two-week Spanish-language-immersion program in Merida. That’s probably what i’d do, maybe get some scuba in while I was there.
I’m not sure I could do that for $3K but I think I could.
I’d go late Spring after the thaw. 
After going to the Travel and Adventure show today, I have to change my choice. Instead of New Zealand I want to visit the Galapagos Islands.
I was planning on hitting Zagreb early next year for a week with about $2000, so 2 weeks and $3000 would probably work. Unfortunately my plans have died a quick death due to screwed up taxes. 
I’d rent an RV and go with my husband on a road trip all over the US.
Sure you can. Granted it isn’t Out of Africa or the African Queen, but camping in the bush? Check. Game walks with elephants, zebras, buffalo, hippos, and the chance for a lion? Check. Beer and Amarula most every night? Check.
Personally, I’d love to go back to Southwest China. That place is a blast.
I’m surprised this hasn’t been asked, but is lodging and airfare already covered? If not, $3,000 can be eaten into very quickly with those things if you’re going abroad.
If airfare and room are covered, I’d do either Dubai or Japan.
If not, California or the Caribbean. Definitely wouldn’t mind seeing Jamaica again.
OP here. Thanks for the great ideas everyone. Thus far I’m leaning toward Italy or that tree-house place in Costa Rica (you sleep in a treehouse! The 8-year old in me thinks that is beyond awesome)
When posting the question, I intended board & travel expenses to need to fit in the $3,000 budget. Granted, I’m the type where if the place and climate permitted, I’d tuck up into a hooded sweatshirt and sleep outside on a few nights if needed. Obviously not preferred, but an option if necessary.
3,000 is more than enough in much of the world. You could do a cheap overland safari out of South Africa for that much, plane tickets included. I saw a chart once of travel costs- a week in Japan will cost you what it will cost to spend a few months in India.
Hostels.com can give you a good view of low-to-mid range accommodations. Don’t let the name fool you…they often cover guesthouses and the like with comfortable private rooms.
Then I think a few posters are going to revising their plans just a bit. Unless someone is extremely adept at hitchhiking, most of the overseas plans will have to be scrapped(you might make it to the Galapagos Islands, but you might have to swim back.)
I would suggest that requiring flights and accommodation in Europe to fit into a €2,269 budget is do-able but very tight indeed, absent an all-in package deal. Allowing about €80 per night for a 2* hotel in Italy and that’s already half the budget gone. Though there are hostels available or maybe couch-surfing.
Large parts of Asia would still be fine for independent travel on that budget. China is particularly cheap for example, and I agree with Ravenman that south-west China is awesome. Yunnan’s really well set up for western travellers too.