cheap boston hotels.. QUICK! thanks! you'll get all the points?

There are no cheap hotels in Boston proper. Check Hotwire.com for some decent discounts. The other option is to look at Hotels in Revere, Quincy, Chelsea and see if you can take the subway in from there.

How do you define "cheap"???????????????

There is nothing "cheap" as one usually defines the term near Quincy Market except for a youth hostel. However there is a European-style hotel of the 1 or 2-star type near North Station named The Shawmut Inn you might check out. It is rated pretty good. Two similar European-style 3-star types, in converted office buildings, exist on Devonshire Street: the Oakwood and Club Quarters, about which I have heard nothing but good reviews, with rooms sometimes in the $ 100 - $ 125 range.