If you are only in town for a few days Midtown is the place to be! Between 46th - 57th and 5t - 7th is the sweet spot. You will be walking distance to broadway shows, central park, amazing restaurants, but it is easy to get downtown and uptown without issues. If the hustle and bustle is not for you then the Upper East side between 59th - 70th and Madison - 3rd is the place for you. The Met is a close walk as is central park, cute coffee shops and restaurants but it will be quieter. You can easily go for a nice walk by the park to end up in Midtown but will be staying with locals. 

Spend the day in Midtown. Explore the New York City Library, Bryant Park, the Moma, Top of the Rock, Grand Central Station, St Patricks Cathedral, the Plaza Hotel (check out the food court downstairs), Central Park, and take in some of the most famous landmarks of Manhattan! The double decker bus tour can also be a great way for you to get a lay of the land. I would then finish the day by grabbing dinner at La Trattoria and going to a broadway show. 
Pro Tip: If you go to Grand Central you can ask a worker to show you where the whisper corner is.

Venture down to the Vessel where you can walk the High line to Chelsea Market, where you can explore Chelsea and the Meatpacking district. You can then continue on the High line to the Hudson River park for a leisure walk to explore. From there you can take an Uber to Chelsea Pier to check out the driving range where you shoot over the Hudson River while looking over New Jersey or you can make your way to the Water Taxi. The Water Taxi is a hop on hop off ride so you can choose a destination you wish to spot at an explore. This is a great day to check out a museum or art gallery if you have this on your to do list and then find a sports game for the evening! 

Explore the financial district and see the Brooklyn Bridge! Get dropped off at First World Trade where you can see the 9/11 memorial and museum. You can then make your way towards the water and walk along the water until you hit Battery Park. Battery Park is a beautiful spot to hangout and relax. Or, you can keep walking to catch the Staten Island Ferry to enjoy the skyline some more. 

Once getting off the Ferry you can make your way to see the Wall Street Bull which is not far from the entrance to the Brooklyn Bridge. If you are wanting to venture into Brooklyn, trying going on a Sunday and check out Smorgasberg which is an amazing food festival.

Explore the upper East Side. This is where you will find lots of high end shops, and lots of locals. The Met is located in the Upper East Side so you can enjoy a walk down Madison to the Museum and the walk the park back to MidTown. I like to do this on my last morning before packing up to head home.