Just bought a ticket to Melbourne. I have NO plans. What should I do?

I'm landing on Jan 1st and leaving 24th, so I have a decent amount of time to travel. I'm fairly used to fast paced trips (1 - 2 days at most in one city) but I'm willing to slow down for this trip. I'm probably going to have about 2,500USD to spend on while I'm there for housing/travel/food.

I've never traveled on my own before - this is definitely a trip for me to experience new things. I'd love to go hiking in beautiful places, meet new friends, and try to see as much as I can with my budget/time.

I'd like to limit my time in the city to a minimum and spend most of my time exploring.

With that in mind does anyone have any suggestions?

Edit: thanks guys for all the replies! Edit2L I'm also open to meeting up with people and traveling with a group for maybe one of the weekends?