what to do? Australia/Asia/Business class tickets? Any tips/suggestions? Thnaks.

Maui.

Most frequent flyers believe that the best use of miles is in obtaining upgraded seats - either using them to upgrade paid coach tickets, or for straight awards for premium-class travel.

Your decision will obviously depend on your travel plans and preferences. If you want to use them for a biz class ticket between Asia and Oz, fine, but I think you'll find that 60K miles doesn't go very far with UA award travel. Europe or Asia upgrades using UA miles usually require that you purchase a more expensive "underlying" fare; the lowest discounted economy fares don't qualify for upgrades.

Consult the award charts at united.com to see how far you can stretch your miles.

Business class to Peru. Imigod, don't waste it on Hawaii. We are saving up our second round of these for business class to Costa Rica. Our daughter is there. Otherwise, it would be Europe. Use them before you lose them.

Business class to Peru is 80K, assuming the OP is flying from North America, so that won't work.

I'm one of those apparently few people who'd rather use miles for free trips rather than upgrades. I do understand that an upgrade is "worth more" in terms of dollars, but I'd rather go twice in economy than once in business. It all depends upon your priorities, how many miles you earn, and how much money you have to spend for paid flights.

Don't rely on booking award travel on the United website, because you can't book there for partner airlines, only for UA (their own metal or codeshares).

Have a few options, dates, etc - since what you want may very well not be available on the dates you need.

Thanks for the feedback. I am in the Northeast US and I would like to travel to someplace I haven't been. I am thinking of going somewhere in Asia.

You're not going to get business class to Asia for 60,000 miles. I'm not even sure if you can get economy to Asia for the 60,000.

You can get RT coach to Japan for 60K with United points (traveling on United or ANA through Star Alliance). The ANA flights go direct nonstop to Narita from Dulles (adn I think JFK too). With United, you have a stop in the U.S. on way there and on way back.