My friends and I are going to rent an apartment for a weekend in Manhattan. Would the northwest corner of the West Village near Chelsea and the Meatpacking District or the border of the East Village/Lower East Side be a better neighborhood to rent an apartment for a weekend?

Better for what?

Since it's likely that there won't be any such apartments when you arrive, the Chelsea location is better because it's closer to some hotels where you might be able to get very expensive last-minute rooms. It also has much better subway access if that's where you end up staying.

See below info from Tripadvisor:

RENTERS BEWARE! Apartment and house vacation rentals are not common in NYC. In fact, most are scams. Even if they are not outright scams, you could end up in an illegal rental and not even know it. Use a hotel instead.

http://www.tripadvisor.com/ShowTopic..._New_York.html

Agree that you need to be extremely cautious when renting in NYC - esp if you use Craig's list. The apartment simply may not exist - or it may be completely different than advertised.

Do this only through a relaible broker. Otherwise you could be illegal (and what do you do if sommething goes wrong with the plumbing or ?) - or simply out on the street.

Renting an apt. for just a weekend makes little sense. The amount you'd save vs. a hotel or b & b is insignificant relative to the chance for being scammed (which is very high).