Welcome! My friend who used to live in Worcester shared this advice on the city:
All of zip code 01602, most of 01603 & 01604 (past #460 grafton st) are nice.
Then there are neighborhoods like Burncoat (01606), Forest / Grove (some of the zip code is 01604 but not all) There are neighborhoods near the Holden line / showcase north that are nice too. The nearby towns of Shrewsbury & Holden are quieter but nice places to live as well.
Stay away from these streets & nbrhds: Dorchester & Providence Sts., Lincoln, Belmont, crystal park area, main south all together & lower may & pleasant street. Really all the streets off of Main St aren't good.
(clark Unversity is just ok)
I has asked her about Pleasant St. She tells me a good rule of thumb is that the pleasant side is from Park Ave & up. It's the lower end that's scary!
Many of the schools have websites listing off campus housing. Here's one of them:
Off Campus Housing
Best of luck!