Australia
Melbourne?
Try Taiwan, Hualien, Cingjing (breath-taking), and Taitung (lost of coastal scenery), lots of scenery.
Air Tickets (Budget): $250-$450 depending on season and promo ($300 spent)
Accommodation: $30-$80 a night depending on where you are staying (dormitory or hotel) ($50x10days=$500 spent)
Transport: Typically you will spend at most $10 a day in big city, $20-$30 a day in more rural areas. Scooter rental is about $15-$25 a day. ($15x10=$150 spent)
Food: $15-$20 a day at food stall ($20x10=$200 spent)
Factor in occasional taxi ($100), train and high speed rail ($100) plus shopping ($200), you are expecting to spent about $1550? Well, just some guideline.
Jeju has really good scenery. But 2 weeks there is a killer.
Dali, Lijiang have really nice scenery as well.
Taroko Gorge, Shi Ti Ping has really awesome scenery too.
And a lot of places in China have really awesome scenery too.