The ultimate UA award itinerary is a routing to Asia via Europe in LH F, with a stopover in Europe. E.g., US-FRA // FRA-HKG // BKK-FRA-US. You get both the LH and TG F lounges with that itinerary. You can do a J version of this that's also pretty nice, flying OS or TK for the TATL.

Or if you want to do Japan, something like US-NRT // NRT-BKK // DPS-SIN-NRT-US. You really can't go wrong flying any of NH/TG/ SQ/OZ/BR in J (though some are better than others on specific routes . . . pick your destinations then come back for more specific advice on carriers and routings).

I would definitely choose a carrier other than UA if you're looking for a special experience.