Like others have said you want to avoid the south Main Street area (main south) for crime, bad parking options etc, and honestly anywhere closer to the interior of the city like Vernon hill, Grafton Hill, Belmont or Lincoln street. They’re definitely not anywhere near as bad crime wise as the rough parts of other cities like NYC, LA or San Francisco but if you have the budget and options I’d choose elsewhere. West side (west of Park Ave) near Worcester State University is pretty good, also Burncoat street area or places on the east side close to Lake Quinsigamond. The new apartments downtown at 145 Front street are nice and have all their own a accommodations like a parking garage but super expensive. Another good option would be looking into apartments in surrounding towns if you want a more suburban setting close to the city - places like Leicester, Holden, West Boylston, or Millbury. Shrewsbury is good too but the further east you go in that direction the rent prices increase dramatically.