We'll be visiting New York for the first time next week and wondered if
we should buy tickets for a musical online or at the theatre.
The only website we've seen so far is Broadway.com so we wondered
if anyone could advise us if this is the best way to do it.
Basically we're looking for tips from experienced travellers.

You can get very good discounts for everything other than the newest,
most popular shows at the TKTS booth:

http://www.tdf.org/tkts/

We have plans to see the regular tourist sites but any insider advice or
tips on what not to miss would be welcome.

There are many very interesting neighborhoods in Brooklyn and Queens
that most tourists miss. Those two boroughs have many of New York's
immigrant communities - Arab (Steinway Street in Astoria and Atlantic
Avenue in Brooklyn), Indian/Pakistani (Jackson Heights), Chinese/Korean
(Flushing) and Russian (Brighton Beach). Williamsburg is an
alternative area full of art galleries and interesting bars and
restaurants, and there is also a thriving art and music scene in Long
Island City, which has great views of the Manhattan skyline.

Two very good underrated museums are the Frick and the Dahesh.

For example...where do the general public head for precisely, to get a good
view of the Macys 4th July Fireworks display, and how early would you
advise us to be in position.

Maybe Long Island City in Queens?