My favorite city ever has to be Vancouver, BC Canada. The city is gorgeous and very clean, if you stay downtown EVERYTHING is within walking distance, you wake up to a view of the mountains, and it's always beautiful weather (though it can be rainy during the summer/fall seasons). Like Poohbear said, there's whale watching, as well as Stanley park, the aquarium (absolutely breathtaking), Gastown/Yaletown (both historical districts; Gastown has become more of a tourist trap, but the architecture is so beautiful, and Yaletown is now sort of an upscale place with restauraunts, independant shops, etc.), lots of plays and productions to see (I saw Evita last year), and an amazingly large chinatown, you could spend a whole day there! Granville isalnd is a must, lots of farmer's markets, shops, events and a beautiful view of the harbour. Walking down Granville street is also great, there's sooo much to see, I didn't even get to take it all in! I may just be biased here, but that's where I would suggest, though it sounds like you're looking for somewhere a little more "exotic".
I've always wanted to go to Kyoto, Japan. Very historical city, the home of the most prosperous Geisha districts (including Gion). It's not as "big" of a city as Tokyo is, so it doesn't seem like you are just in another metropolis. There's a good combo of city and country. At any rate, I have a bit of a love affair with Japan, but when you're there, you can pretty much take a bullet train out to the cities, country, and there is so much to see and do. You can spend a day in the
onsen (hot springs) in the mountains, or spend some time on historical tours, attend cultural festivals, etc. etc.
I've also always wanted to spend some time in New Zealand, Portugal, Italy, the Dominican Republic....ahhh so much to see and do and so little money with which to do it all
I hope you find a place that's just right for you, Good luck Piglet (and take lots of pictures so you can show off to us when you get back!)