Do anybody know anyone who have a apartment for rent in the boston area for not that much?

try looking here http://www.goDuru.com ...good luck

Which Boston ? Lincs or Mass ?

If the local newspapers and web aren't helping check with local real estate offices. Many agents have rentals and/or know of people they have sold investment properties to for rental purposes. You could probably start at realtor.com since it's the weeked though.

www.thegumtree.co.uk

houseladder.co.uk

availablehouse.com

local papers - some available to view online