Exciting news and congratulations - Pittsburgh is a great school. Pittsburgh has really become a pretty cool town, cleaned up a lot from when it was just "steel town". Good sports town. There's good fishing/hunting opportunities all over the state. Climate may take you some getting use to, you will certainly experience 4 full seasons (which I like). Cost of living overall is probably cheaper, though electricity here in PA is getting stupid (if possible, get something with gas heat).
My recommendation - DO NOT use a conventional moving company - if you have more than you can move by yourselves (in U-haul/Penskey-type rental) go PODS or something similar - far cheeper, you pack your own stuff in the POD, rather than a conventional mover who will throw your boxes, pile heavier boxes on boxes and if any storage is involved, crush multiple boxes (this I know from our move from Bend to North Carolina - conventional which cost close to $20K, and our move from NC to the Poconos using PODS - about $3K)
The big question, which is largely unanswerable 'cause you just never know, is what you will do and where you will be after the wife finishes her program. This makes for a hard decision on what to do with your current house, but if you decide to rent your place, just be sure the rental income is greater than all current payments (mortgage, taxes, insurance, etc and any property management costs if you use a property management firm) - you don't want to be burning money on 2 residences. Equivalent neighborhoods, cost of housing/renting will be cheaper than the PNW.
Good luck with everything, and welcome to PA and the northeast!!!