Where to stay?
If cost isn't an issue, you could always stay in a nice place in the city. A very nice hotel would cost you about 150USD per night. A motel in the suburbs would probably be closer to 25USD.
What to do?
The question is, what sort of thing are you into? I guess the ankle problem will mean you would be generally limited to looking at things rather than doing stuff? Will you have a car?
I can guide you a little bit from the Melbourne point of view. Although, I haven't really been a tourist here, so it's a bit hard knowing what sort of thing to see. I can think of lots of things, but they're not necessarily what a visitor would want to do.
There are (is there an abbreviation for "there are"? ther're??) lots of nice drives around Melbourne, with various parks and things. No real mountains in Australia (by international standards), but some very happy coastline within three hours of Melbourne.
Then there's always the penguins at Philip Island!
If you're into the performing arts at all, then there would be plenty to do. I guess that's not a very touristy thing to do though, because it's not distinctly Australian. Lots of nice food, too, which might be worth trying, given that my friends who now live in the US tell me they miss it.
Then, of course, there's the international brethren (in a non-gender-specific sense) of empeg owners, members of which I'm sure would be happy to take you to their favourite places.
Maybe it's best if, when you figure out where you'll be, you post again. If Melbourne features on your itinerary, I'd be happy to help, to whatever extent I can.
Richard.