I heartily agree with the Koh Samui or Bali suggestions. We've been to the excellent Conrad Bali and will be going to the very nice looking Conrad Koh Samui later this month. Between the two, the CKS looks even nicer as a place to just get away and relax, as the rooms are all standalone hillside villas with their own decent-sized infinity pools. CB better if it's a priority for you to be able to walk to some other places to eat (which I understand you can't do from CKS) and if you want to take day trips (easily arranged with lots of reliable drivers there) to explore the beautiful island and culture of Bali, which retains more of its original identify than Koh Samui does. From what I can tell, I'd recommend CKS, but will have a firmer sense after actually visiting there.
If you do go to one place or the other, you could stop off in Bangkok or Singapore for a night or two, which would be fun. Make sure you leave lots of time for connections from UA to whichever airline you fly to the final destination (and vice versa), as you'll be on two different tickets.
As a HH Gold, you should free breakfasts for two included in both places.
One thing I'll emphasize is getting your UA tickets way in advance (which increases the chances of upgrades being available) and only doing so if the upgrades are available at time of ticketing. If you simply wait list for an upgrade you're very likely to be disappointed. To put it mildly, UA is not great on making international upgrades available, so starting to search ASAP and being flexible about your travel dates will be necessary.
It's also helpful is to book your hotel rooms way in advance, especially for the CKS as availability at normal award rates (as opposed to astronomical redemption rates) can start disappearing months in advance for that property.
Finally, be aware of what the climate is like in these places. For example, the US autumn is the rainy season for Koh Samui and our winter is the rainy season for Bali. You have a chance of some sun during those times, but also a chance of lots of rain. Here's a good site for checking out what precipitation and temperatures are like around the world at various times of year:
http://www.worldclimateguide.co.uk/
Happy trails!