Another vote for Argentina. Add to its pluses that it won’t be too many timezones away from you (I am assuming you are in the US), so no jet lag to worry about. The flight is wicked long, but so is the case for most other detinations suggested.
And if you are going down there, it would be a shame if you didn’t include Santiago (Chile) in your itinerary. Maybe some Peru thrown in for good measure?
Have you thought about Aruba? We go down there every year, and it’s wonderful! The people are the friendliest we have ever met, and most are extremely well-educated (3 official languages learned in school- English, Dutch and Spanish, plus papiemento and usually German).
The food is fantastic (must love seafood), the beaches are lovely, and the windward side of the island is barren but beautiful. It is always warm and usually sunny, but with a near-constant breeze. No humidity, no bugs. It’s not a place for people looking for lots to do, but it’s a wonderful place to relax.
I highly recommend it.
I also love Barcelona, Hawai’i and Mexico.
Now, I want to go to Turkey. That’s on my short list of places to go in the next 5 years anyway.
I recently visited South Africa. But, if you’re only going for a week, that’s a long-ass ways away.
Still, it’s pretty sweet. It will be warm. Easy to get around. You can take a dip in the Indian Ocean. Cape Town is pretty damn cool.
I’ll throw in a vote for SE Asia, although it’s a long flight for a week. It will certainly be warm there, and there is much to see in the way museum and very different architecture. Plus, lots of good eating, especially if you’re adventurous! As to specific countries, I’d recommend:
Thailand - lots of people aren’t particularly enthusiastic about Bangkok, but I think it’s a great city. Chiang Mai is widely agreed to be lovely, and there are many nice beaches in Thailand for a little R&R. Lots of great architecture (the Royal Palace, all the wats (temples), Jim Thompson’s house).
Vietnam - Such good food! And so inexpensive! Lots of Vietnamese food, as you would expect, but also really great French food. Yum. The French colonial cities are beautifully designed architecture-wise, if a bit run down. Shopping is fabulous there. Halong Bay is supposed to be gorgeous. The Cu Chi tunnels and the musuem on the Vietnam War are both very interesting.
Cambodia - I was there in 1999, and from what I understand it’s a bit less scary and more touristy now. Angkor Wat and the other temples in Siem Reap are the most spectacular thing I’ve ever seen.
Make it a ten day trip and spend a day or two on a beach in Thailand recovering from jet lag, go explore the temples in Cambodia for three days, and then spend a few days in Bangkok or Chaing Mai buying souvenirs.
I have such travel envy! Enjoy your travel planning!
PS. I’ll second or third votes for New Zealand, too. Such a beautiful country!
Last I heard, there was a lot of civil unrest in Oaxaca. True that was a few months ago, but it’s off my list to revist for a few years. We went through San Cristobal de las Casas and it was just creepy with all the rebals there in the town square. Only time on the whole trip I was worried about safety.
Much as I love the D.C. area, I would urge you to eschew Mr. Excellent’s advice. If you’re gonna come here, do so in May or September, when the weather’s temperate but the kids are in school. D.C. in January and February can be just awful if you’re here on a bad week, weather-wise.
Lok mentioned Maui, and I’ll second that. South Maui especially has a wide variety of great beaches within a very short distance of one another - big beaches, pocket beaches, beaches with regular sand, or with red or black sand, beaches where you wear a bathing suit, and beaches where you don’t.
Weather’s great anytime of year. If your mom’s up to snorkeling or scuba-diving, it’s a good place for that, too.
You wouldn’t go to Maui for the food, but once you’re there, it’s pretty good actually. Mama’s Fish House on the north coast is one of the best restaurants my wife and I have ever been to. (Not a luau, just a very very good restaurant.) But unless you’ve got an unlimited budget, you’ll only eat there once during your stay. Quite a variety of ethnic restaurants which hold their own. I’ve had very good Thai and Tex-Mex there, among other cuisines.
Maui Revealed is the essential guidebook to the island.
Why has no-one suggested London??? One of the largest, oldest and most individual cities in the world!
[ul]
[li]You can’t walk for two minute without stumbling across a site of historical interest or museum.[/li][li]Every cuisine in the entire world is here.[/li][li]It has a very good transport system, including buses for people with limited mobility (stay away from the cabs as you’ll get ripped off).[/li][li]Some of the best theatre productions in the world - Shaftesbury Avenue is the European equivalent of Broadway.[/li][/ul]
I admit it’s not very warm, your Spanish won’t get particularly well utilised and you’ll get fairly screwed on the exchange rate.
Failing that I’d second people who suggest Spain, particularly Barcelona which is one of the most cultural sites in all of Europe.
I second the Maui Revealed book. They consistently were right on the money about food, sights, and things to do and see when I was there. I kept running into other people there also using the book while seeing different things than I was and they reported the same experience. Any trip I make to Hawai’i will be made using their books for any island I am visiting. Old Lahaina Luau had great food, a good show, and an open bar. The bar was mostly wasted on me since I don’t drink, but the others at my table seemed to enjoy it. 
So far I’m leaning towards Greece, Spain, Argentina and Turkey. I’d LOVE to go to Costa Rica, but what I really want to do there is snorkeling and hiking, and mom might not be up for much of that. Panana I hadn’t thought of. Anyone know anything about Puerto Rico?
EJsGirl, I have been to Aruba and it was great, like you said. I think there’s plenty to do there for a week; I went horseback riding, rode dune buggies, toured the island, and snorkeled. Maui I’ve been to a couple times…I do love it, but maybe someplace new this trip. My mom’s company has an office in London that she goes to all the time, so she’d probably like to go someplace different for a vacation.
Thanks all for the advice!
We had a recent thread about vacationing in PR.
http://boards.straightdope.com/sdmb/showthread.php?t=443204&highlight=vacation+puerto+rico
It would depend on what type of activities would your mom enjoy. It sounds like you would be more into sightseeing, museums and fine dining. I am not sure PR is the place for this (not for a long vacation, anyways). PR is more of an adventure destination. If you are going to South America, many airlines will make a stop in San Juan, though. You might want to schedule it as a 2-3 days stop and enjoy Old San Juan, and maybe a couple of days in a nice beach hotel, if your destination is more of a mountain/city place.
Me, too, and it’s a country that I’ve never considered before.
For the OP, if not Turkey, then I concur with Costa Rica. I’ll even plug the travel agency we used: Adventure Life. They handled everything except the plane, and they make sure that the majority of the places they deal with have someone who speaks English. We spent four days at a ranch in the jungle called Selva Bananito Lodge (website has sound), which I cannot recommend highly enough, and then a place in Port Limon called Cariblue (also with sound), which I didn’t care for (but I’m not a beach person.) The food at Cariblue was great, though.