My 1st house in Los Lagos was $500 USD/month and I got that house through the school. You pay 1 month deposit + 4 months rent when you move in. All the student houses are furnished.
In my 2nd semester, I found a better house in Los Lagos on my own. It was $600 USD/month but it had AC, bath tub, electric stove, washer & dryer. It was nice.
I think it was pretty much safe in Los Lagos. Just make sure your house has window burglar bars.
There are some nice restaurants in Belize City. You can also visit San Pedro or Caye Caulker if you have time.