Actually, you can do all of the things on your list on one day in NYC (well, I'd just do ONE show and ONE dinner

) but it ceertainly is best to spread your vaction out over several days.
A great public transportation system and close proximity for everything you've mentioned really do make it possible...
Just last Monday, I went into the City (I live out on Long Island) and, from 1030am to 4pm, I packed in the following:
-getting an eyeful of the glorious Empire State Building and the Chrysler Building, two of the most beautiful architectural structures in NY
-shopping on 5th Avenue
-viewing of beautiful Christmas windows at all the high end department stores
-visit to St Patricks Cathedral
-visit to Rockefeller Center to see the Christmas Tree and ice skaters
-wonderful leisurely lunch with wine at Cite'
-shopping in Times Square
-cab downtown to Spring Street to have dessert (Rice to Riches, a rice pudding emporium that is DIVINE!)
and yes, that was just in a few hours....and we could've fit in a show, dinner and a nice hotel stay if we'd been inclined.
But I certainly suggest taking as much time as you can....a week is not too much....and better to take a few days that don't fall on the weekends, as crowds are noticeably less during the week if you are doing the touristy things.
Do plan ahead...be flexible, but know what are your "must-do's", so that you don't get sidetracked (which is SO easy) and end up missing what you truly came for. Also prepare for the possibilty of bad weather and think of what indoor activities you'd like to do.
And, most especially....HAVE FUN !