Australia is a very popular gay tourist destination. For almost everyone it's a very long travel to get there and with the many time zones difference it takes some time to get used to the time difference. So you usually don't do a weekend Australia, but at least 2 or 3 weeks. Fortunately there is plenty to do and visit.
From Europe there are no direct flights to Australia. Flights often go via Bangkok, Singapore, Hong Kong or other cities in Asia. At a little extra cost you usually can make a stopover for a few days in on of these cities. This can be a great extend to your holiday!
Panama City has about 4 large gay clubs and a gay sauna. The gay night life is focussed on the weekend. Many guys from Panama are not openly gay and discrete, and you will find them at several gay friendly places.
Bocas del Toro has no gay places, but many nice restaurants and boutique hotels facing the ocean, beautiful beaches and is next to San Blas the most popular Panama beach destination.
Boquete is a very beautiful relaxing area with a very mild climated in the highest part of Panamá. It has no gay places, but very nice boutique hotels, restaurants and is a perfect place to relax a few days.