Mr. Richards:
I grew up in Pittsburgh and played Fox Chapel, Oakmont, Field Club and Longue Vue as a boy in the 1950's and a young man in the 1960's. I still play Fox Chapel once or twice a year, and Oakmont once in a while. Fox Chapel is a wonderful course (all except the 8th hole, which has been tweaked and moved back and forth between a par 4 and 5, but just has difficult topography.) It was fixed up in subtle ways for the Curtis Cup, and in particular the tree removal program was very effective, aesthetically and for quality of play. Fox Chapel has archetypical and well preserved Raynor greenside bunkers, and every hole requires thought and a variety of shots. The conditioning is always good and the view from the porch overlooking the course is one of the most glorious in all of golf. Play it if you can.
I haven't played Oakmont since they took the trees out, but all reports are good, and they know how to run a golfer's club, so it must still be great. Longue View is a quirky course, much more hilly than Field Club, Fox Chapel or Oakmont, but a friend who is a member tells me that it's really well conditioned these days--not always the case in the past.
Allegheny is also a good course--it's a very private, old money place whose members I'm sure would not care a whit whether they were on someone's list of excellent courses.
I doubt the assertion on the thread that some of these clubs have a regular "reciprocity" arrangement that other cities should emulate. Fox Chapel--a place where you can walk out on a Saturday with no tee time and just play away--is a very private place, as is Oakmont. I can't imagine that they just let members of another club show up and play without being with a member.
If you get to Northeast Pa., try Eagles Mere Country Club in Eagles Mere, Pa. on a mountain top north and east of Williamsport. It's a 6100 yard Flynn course, built in the 1920's for the hotels that were then a favored Philadelphia resort. It's a lovely mountain course. The routing has not been changed since it was built, and the greens and (limited) bunkering are also pretty much original. It's not a great course, but is a slice in time that's hard to find.
I've never played Latrobe, but how could you not play Arnie's course. I plan to.
Good luck.