I'm assuming you're meaning US summer, i.e. June-August kinda timing?
What are your hobbies? Do you like hiking? (Or trekking, backpacking... whatever you want to call it, overnight walking) If so, lots of options at that time of year. Ever been to India before? Ladakh is great around then. Rest of the Himalayas are in the monsoon, but Ladakh is in the rain shadow, so remains dry and fairly stable weather-wise. Could go to Greenland, the Lofoten Islands or the Faroe Islands if you're wanting somewhere a little different in Europe.
If you're headed to Australia, that's the best time of year to see the north as it's the dry season. Good time to visit Cairns, see the reef etc. Less good to be further down south, though anything in NSW and above will probably be fine. Weather tends to get worse and colder as you head south. Tassie (where I'm from) is great, but best seen in the summer when you can spend more time outside.
Also a good time to be in the central andes - e.g. walks to the Cordilleras Blanca y Huayhuash out of Huaraz, the Cordillera Real in Bolivia etc. Go and see the salt flats, the Atacama etc.