Which suburbs are recommended for new people coming to Melbourne?

Hi April, there are a number of places you can move to within your rental price range. Melbourne is quite diverse with a large number of residential properties/communities within the CBD fringe and generally quite safe at all time, (of course that doesn't mean you go wondering into dark alleys late at night). You will find plenty of rental accommodation of 1 bedroom places within the CBD fringe, mostly housed by younger people/students that go to one of the universities. a quieter place would be Docklands or Southbank, just on the fringe of the city. Hope this helps and good luck.

Hi April, for what you're after I'd recommend checking out apartments for rent in Richmond, St Kilda, South Yarra and Prahran. These areas have a lot of new modern apartment buildings with great views, easy access to public transport, close to the city and shops, gyms, cafes and restaurants. South Yarra and Prahran have great shopping, cinemas, cafe culture and gyms. St Kilda is a bit more laid back and close to the bay so you have great views. Richmond is right next to Melbourne's sporting entertainment precinct, has a lot of live music venues and has good shopping options.
Best of luck with the move!

I'd agree that St. Kilda could be what you're looking for. You can also try Windsor. Docklands is newer but a little sterile IMHO. It is close to transit and shopping though.

Doncaster!!! Only 14.5 kms to Melbourne CBD. Stunning place to live and well-serviced ... Spoiled for choices. Check it out.

Hey April

Have a quick read of this, someone put together some info for people looking for the kind of places you mentioned.

http://www.homely.com.au/melbourne-greater-victoria/questions/best-suburbs-for-young-people-moving-to-the-city#question