From Wiki

If looking to live near NY city, a strong suggest that you check out Hoboken, just across the Hudson River in NJ......large number of young British expats living there (some even post here!) as it is cheaper than living in NYC but very trendy and vibrant....and rapidly becoming 'gentrified'....there is a new 'W' Hotel being constructed there.

You just take the PATH subway train (runs all night) to various stations in Manhatten, the NY Waterway ferries or the buses to the Port Authority, one block from Times Square.

Some links (with rental listings):

Washingtonpost

Hoboken

Hobokeni

Pub with live bands:

Maxwells