the town of malden. orange line subway to downtown.

it's a relatively safe and inexpensive place to live. with this budget you can try malden garden, or the gateway apartments. they may have referal discount( refered by a tenant, the tenant get $$, then you and that tenant can split $$), or sometimes 1 or 2 months free with one year contract.

to find out more about boston's convenient subway, google mbta. Then you'll have some idea about boston's vicinity area.
It's a great city, with many activities fit for young people.good luck!