Good luck with finding a 1-BR for <$1200 a month

The cost of housing is probably the biggest sticker shock you'll be hit with when you land here. Few
studios rent for that little. But Simmons probably has an off-campus housing office (or at least a desk within an office) where you could look over listings for places. Often faculty members at a college are happy to offer spare living space in a large house, or an "in-law apartment," to students of their school. You might also be able to set up a barter arrangement whereby you'd make grocery runs, mow the lawn, etc in exchange for paying less per month.
Here are neighborhoods to avoid, and why:
Allston (south of the turnpike) - Student Ghetto Central, with
the highest crime rate in the city thanks to lots of B & E's and late-night street fights and fun stuff like that. Like NYC, it's a nice place to visit but you so don't want to live there. Enjoy the great variety of funky stores and "ethnic" restaurants - not to mention a couple of my personal favorite spots (Harpers Ferry for blues and alt-rock shows, and Sports Depot for tasty bar food and guess what else.) But be outta there before midnight.
Mission Hill - A challenger to the Student Ghetto Central title thanks to skyrocketing rents closer in to town in the South End and the Fenway. The community declined steadily for decades after WWII but has rebounded since its big public-housing "development" was knocked down in favor of "mixed-income" townhouses. But there's still an edgy feel to it, which only increases the farther away from Huntington Ave you go. This is an overstatement but not entirely off the mark: if you're not dodging muggers in Mission Hill, you're dodging "missiles" thrown by partying undergrads while their compatriots stagger and puke and everybody shrieks.
"Better," relatively convenient, communities are Jamaica Plain + Brookline + Allston north of the turnpike + Cambridge. However, rents are prohibitive unless you're connected.

Your best bet for finding a decent and affordable place would be in northern Dorchester, in the neighborhoods flanking Dorchester Ave (aka "Dot Av") near the Savin Hill and JFK/UMass subway stations. Bus route 8, out of JFK/UMass, even travels Brookline Ave right by Simmons on its way to Kenmore Square. The main downside to this area is that most of the rental units are in "three-decka" buildings - way more space than you'd need.
Sorry to not be more encouraging...