New York

Have a look at the High Line, it is cool - a walkway above the city.

I lived for a long time in New York City , stay away from all the tourist traps around Time Square, Broadway when it comes to restaurants. There are nice hidden eateries around E 56th towards the East River where most people make a wrong judgement from seeing the outside .

A few years ago now but we visited a full-on gospel service in Greater File Baptist Church Harlem, walked the Brooklyn bridge, saw a basketball game in MSG, walked central park - took a boat on the lake, watched filming there, met Lennox Lewis and listened to the blue vipers of Brooklyn, saw the bling of Trump Towers, had coffee in the crazy Viand 61st Street and a ridiculous bagel in Wall St, sat in Grand Central Station, TKTS booth in Times Square for last minute show tickets, did the Staten Island ferry thing (dirty windows ), couldn't see any point in paying lots of money to climb into the statue of liberty and look out through a little hole. Did a lot of pootling around just taking it in and reading Tripadvisor. Went on some 'free' walking tours. Avoid Times Square and tourist areas for food - there are SO many brilliant places/street food in any cuisine you want but none in Times Square. Wandered around some of the different areas of NYC. Underground is OK but not near as good as a typical European city. Taxis can be a decent way to go but best up/down not side to side and deffo not at rush hour. We were there before Uber. Prepare to walk. Contrary to myth, we found New Yorkers very friendly (outside the main tourist zones and when they aren't in a hurry!)- Just engage and tell them how much you love the city. Don't get into politics or similar - very polarised. Avoid talking gun control or religion. Very helpful and keen to give advice.

PS - how could I forget Ellen's Stardust Diner in Times Square - really contrived, mediocre food but an experience your daughter should love. May need to book ahead (edited)

Sounds obvious but walk... walk... walk. Manhattan is just under 14 miles long and just over 2 miles wide. You can see so so much and stumble across amazing sights and experiences just strolling about. Take comfortable shoes and have a supply of compeed on hand just in case.

Contradicting my walk advice - make sure you get out of Manhattan too if you can and go and check out DUMBO and other parts of Brooklyn like Williamsburg/Bedford Ave which are well worth a visit. You'll be absolutely spoilt for choice on places and things to eat, drink and things to go and see, so try and prioritise.

Not sure how old your daughter is, but if she's +21, to save a few pennies there is a big happy hour scene and plenty of resources online to check when/where some are.

So many obsess about going up the Empire State Building - I've always preferred 'Top of the Roc' as I think it's a better view, but each to their own. Top of The Roc has better views of Central Park.

Have an amazing time!