I'm from Singapore.I actually did a one month backpacking trip in Asia in Nov 2016
I highly suggest you check out Air Asia ASEAN Pass if you're looking to hop to many places in Asia ( can't paste a link to it cause I'm a newbie )
With the ASEAN pass I actually went from Singapore > kl > Nepal (separate flight tix/round trip )>kl> Phuket > Vietnam >Bali >back to Singapore .
Total expenditure for flights cost me SGD$800 only .
Place in Asia that I recommend:
Singapore
Was born here. Very safe country, My Sister could walk at 3 am without worrying about getting mugged but it's a very expensive country.
Vietnam
Mui Ne , 4 hour train ride from Ho Chi Minh, a quiet fishing village , you could check out the red sand dunes and the white sand dunes.Half day jeep tour to the dunes is only USD7/pax
Phuket
Island hopping !For about 30 usd/PAx (I can't really remember the exact fee )you can get a full day island hopping tour and water activities like snorkeling /Kayaking /Canoeing . Depends on the package you take.
Bali
Didn't do much nature activity here except for mountain tracking but it's a beautiful place to be and I hope you research this place
Nepal (South Asia )
Trek for 10 days here to the base of Mount Everest !