I am based in the US, and have a .com domain (let's just say it's widgets.com). If I want to rank in Australia for keywords, can I just buy another domain (say widgetsAU.com) on a local hosting company in Australia instead of widgets.com.au. So, my question is, how much does that .com.au domain really impact SEO? I am asking because in order to get the .com.au extension you must register as a foreign company in Australia, which is very expensive

It will not give you a big advantage.All the extensions are not so important for SEO - just try to get more backlinks from Australian sits....

Purchasing domain is not only solution for you. You can get traffic and business from Australia by targeting your website there and by creating back links on the sites which target there. You can also set your Geographical target in Australia.

Having .Au domain has its own impact. If you have that one then you can easily target both your audience and area. But as you told you have .com domain and want to use same one for australia then you have to work more for that. As you have to list your business on Au ranked sites so that people will aware about that. Try to post your unique content on au hosted sites related to your website.