hi, i am technically not a new yorker but work next to the rock and live just outside the city in nj. i have to say i am cheesy and super excited that christmas is coming. that week is busy, but not as busy as christmas week or the week before in my opinion. working next to the tree for 4 years i have a good idea of the crowds lol.
definitely figure out the subway, some times of day you can't take a taxi and you can't walk everywhere. many new yorkers are nice, i often give directions myself, so find a friendly face and ask if you are really unsure. i recommend stop hop as well. a lot of great restaurants are downtown too, so its worth it to learn to move around.
if you are going to the rockettes and top of the rock for a budget lunch check out the concourse below. some of the lunch places have long lines but great food (hale and hearty soup is my favorite). you may have a hard time finding a table, but if you go off peak (11 amish or after 2 pm) sometimes you can find a table near the ice rink. its basically like a fancier food court.
to get a great picture of the tree you can stand in front, or if you go the side towards 48th across the st, you get more of the tree.
st. patrick's is right there and while under restoration it is just gorgeous. the stained glass is hard to see inside with the scaffolding, i suggest going to the back of the church (madison ave) to take a peak. tourists rarely go there but the back is actually pretty amazing too, plus there is this hotel across the street with a really pretty courtyard and normally they put up a nice tree. saks fifth avenue is next door. some of the more spectacular windows start here, so my advice for a tour of 5th windows is to start at saks and go up to the park. below saks you have a lot of regular stores (build a bear, guess, fossil etc). you will pass a lot of the luxury jewelers (tiffany's, cartier). henri bendel and bergdorff's are also up there with great windows at the holidays. that corner of the park is where you will see the plaza (reminds me of home alone 2 in the winter) and fao schwartz). that corner of the park is nice too and easy to go in for a quick stroll. if you go down 57th you can window shop in a lot of luxury stores, some have amazing windows too.
as for souvenirs saks, macys, and henri bendel's have cute little store branded momentos like makeup bags and ornaments. i think they are much cuter than anything found in a tourist shop. macys i discovered has this shop in the basement, and they had everything from makeup bags to aprons!
the holiday shops at bryant park are ok, some are just stuff you find at street fairs. keep in mind times square is mostly a mall at this point, the
disney store has some nyc things on the first floor but most of the items are things you find in any other store.
the met museum has some gorgeous tiffany art in the american wing. its suggested donation so if you want to go for an hour and don't want to spend the price, you can at the counter offer less and get admission.
in times square a hidden gem if you like to check out church's is st.malachy's.
http://www.actorschapel.org/
My DGM passed away in May and her birthday is that weekend, so I thought it would be nice to get away. Do I need to have an itinerary like Disney, or can we just play it by ear? Any suggestions would be greatly appreciated.
Corner of Broadway & 51st Street.
. As another poster said, hopstop is a great app to help you navigate the subway system, as it can be a bit overwhelming. I would also use hopstop to figure out the approximate cost of a taxi from LGA, there is a tool to do so on there. Thanksgiving weekend will be extremely busy, but it is also a really great time to visit because there is so much going on. 
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