What are some free and inexpensive things to do in or around Pittsburgh?

There are free tours of the Allegheny Observatory and you can look through the same telescope that proved the rings of Saturn were not solid back in the 19th century.  There is also a free walking tour of the Battle of Homestead Historic Site. Get a downloadable brochure and audio file here (http://www.touranytime.org/tours/battle/) around the Waterfont area with shopping, restaurants and bars.

The Three River's Arts Festival begins June 6-14th. Free concerts through out plus great visual arts all in the Downtown area. Just fun to go sit at the point & relax on the grass. Many vendors for food & crafts but it is all free open to the public. 

Take the Duquesne Incline up to the top of Mt Washington-the views of the city and the three rivers are spectacular.  If the Pirates are in town, PNC Park is one of the most beautiful ballparks in the US, plus I love when the close the Roberto Clemente Bridge to traffic on game day, and everyone floods across!  Nose bleeds seats are very affordable.  Make sure to stop and order sandwhiches from any of the Primanti Bros. (they sell them at the ballpark too) locations-order the original, the fries are magical.

The Carnegie Museum of Natural History was legendary to me when I was young. 

And make room in your stomach for a walk along Strip District, especially if you have some Polish roots.  Lively, historic and entertaining!