Best things to do in New York City?

I'm going to New York in August and I was wondering if anyone has any recommendations of places to visit and things to see, particularly things that aren't the obvious tourist attractions.

Assuming you mean New York City:

Take the cable car ("aerial tramway") to Roosevelt Island. Manhattan teminus is at 60th St and 2nd Ave. It's a nice walk around the island (well. it was when I did it in 2011). https://en.wikipedia.org/wiki/Roosevelt_Island_Tramway

Visit the the 14th Street/8th Avenue subway station (A/C/E/L trains) and look at the "Life Underground" throughout the station complex. https://en.wikipedia.org/wiki/Life_Underground

Admire the interior at Grand Central Station.

New York Transit Museum (if you're into that sort of thing): https://www.nytransitmuseum.org/

Travel on the Staten Island Ferry (which is free) -- you get quite a good view of the Statue of Liberty from the ferry.

The High Line is an "elevated park" built on an old elevated railway line. https://www.thehighline.org/

"Top of the Rock" at the Rockefeller Center is very similar to the Empire State Building and less well known, so quieter. If you're planning to go to either, check to see when the quiet times are -- otherwise you end up being in a queue to get into the building, to join a queue to go through security, then to another queue for lifts, etc.

Don't forget that New York City is more than just Manhattan -- there's stuff to do in the other boroughs too (Queens, Bronx, Brooklyn, Staten Island). The Brooklyn Museum is good.

Don't rely on taxis, use the Subway and/or buses. Read up on how the subway works. It helps to remember that references (in Manhattan) to "Uptown" means "higher street numbers" and "Downtown" means "lower street numbers" (e.g. if you're at 50th Street station and want to get to 103rd Street station, you'd be looking for "Uptown" on the station signage; for 14th Street it would be "Downtown"). There's almost certainly videos on Youtube explaining the subway. Note that the Metrocard is on its way out, being replaced by OMNY. Contactless cards work too (as on the London Underground), but make sure you're using a card that has low foreign exchange fees. I got a Halifax Clarity credit card specifically for this reason.

If you're in NYC for long enough that you fancy a side-trip to Washington DC, there are some suprisingly cheap fares if you're happy travelling on Amtrak outside peak times (i.e. leaving NYC really early in the morning and returing late evening). You do need to book well in advance.

To add to what I wrote before:

(1) The MyMTA app is really useful to have for the subway.

(2) When planning what to do, look up the opening hours for things like museums -- New York might be "the city that never sleeps", but that doesn't mean that museums (for example) don't close at 5pm. Plus places might not be open 7 days a week.

I've only been once very briefly but - as a music student - I enjoyed walking around Harlem and going for food at this place: https://www.redroosterharlem.com/ .

Also enjoyed seeing 'Annie' on Broadway but that was expensive (and is very obviously tourist-y)

I would love to see something on Broadway, it sounds amazing! We were thinking about seeing if we could get some cheaper tickets for a show on the day because I think there's a couple of ticket offices and stuff like that where you can grab a last minute deal.

Do it! But maybe have a shortlist of, say, three shows you'd like to see/wouldn't mind seeing. I think the reason it ended up being so expensive for me and my sister was we went to the last-min ticket booth in Times Square quite late in the day, and I refused to see anything but Annie

I'm such a massive musical theatre nerd, so I'm not sure I'm gonna be able to narrow it down lol. We'll probably end up going for whatever is cheapest. We are staying somewhere near Times Square so we should be able to get there early and get a good deal.

I think we're gonna try and plan an itinerary before we go, to make sure we don't get anywhere and discover that it is closed, and so we aren't overwhelmed with choices of things to do when we arrive. We are going for 4 nights but we don't arrive until dinner time on the 1st day so probably won't get anything done. Thanks for the suggestion about the subway app.