If you can go thru Hong Kong or Bangkok, they're both dramatic and
scenic cities (and major airline hubs).
But, others may suggest many other good ideas also.
You might want to check the United Website (or the Star Alliance website) -
they used to allow one stopover; I don't know if that is still true. But
United's routing to Singapore would be through either Tokyo or Hong Kong.
You might also check on a possible Star Alliance award using your miles on
either Asiana, All Nippon (ANA), Thai, or Singapore Air, all of whom are in
the same alliance with United.
A good place to research this is also the Flyertalk website,
www.flyertalk.com - in the United forum.
Jeff