"Wheah you go to buy beah."
--The Wicked Good Guide to Boston English
The word "packie" is a New England term for a liquor store. It's short for "package store", which is defined as "A place which sells prepackaged alcoholic beverages for consumption elsewhere".
There are plenty of liquor stores which call themselves liquor stores; these are usually your standard, well-lit, medium-to-large liquor stores. A packie is usually a small, cramped place, called something like "Mike's Package Store", with low prices advertised in 3-foot-tall letters on paper signs which cover all the windows. Nine times out of ten, the guy behind the counter will be Mike, or a relative of his.
Since Massachusetts blue laws dictate that you can't sell alcohol in supermarkets1, when you need beer or liquor (especially cheap beer or plastic-bottle liquor) quick and with a minimum of hassle, you make a packie run. If you're looking for a place that has fancy-schmancy stuff like non-boxed wine and cognac, go to a liquor store, you yuppie scumbag.
1I guess it isn't technically illegal, but they never give licenses for it.