What are the best things to do, see, experience, and eat in Newark?

Definitely check out the Ironbound District- the Portuguese section of the city.  It is on one side of Penn Station along Ferry Street.  There are a bunch of barbecue and tapas places, but my favorite is Mi Pequeno Mexico which is a great but totally not fancy Mexican restaurant.  

In season, it is fun to watch the Red Bulls play soccer at Red Bull Arena - this is only a short walk across a bridge from the Iron Bound. 

Newark also boasts McGovern's Tavern - be sure to order the lava fries - mozzarella fries with buffalo sauce - who knew?

Another option is to do the Philip Roth Newark tour.  Go to Weequahic High School - Roth's alma mater.  Check out the neighborhood that was primarily Jewish from the '30s to the '50s.  You can also check out the The Newark Public Librarywhere Neil Klugman, main character of Goodbye Columbus, works.  The Library has a world class collection of modern and contemporary prints.

Lastly, you might want to check out the Cathedral Basilica of the Sacred Heart.  

Branch Brook Park is really beautiful in summer months and into fall. Not sure if this was the park you were mentioning. Walking in the  Harold Parker State Forest is really pretty too!