We did this trip last year and loved it (looking at going again this year).
In Edinburgh you have so much to do, it's impossible to think where to start. We've done the Castle before, so this time went to see the Royal Yacht Britannia, then strolled along the Royal Mile. It was just before the G8 conference, so a lot of things weer closed off, but it's a great walk.
Glasgow we were very dissapointed with, the city was very drab & uninspiring (although I have to say the rain didn't help). We saw all the advertised sights & aren't planning on rushing back. I think it's certainly doing some research before joining the ship (try http://www.seeglasgow.com
We visited Invergordon a few years back, and were treated to local entertainment & food. Although this was probably more to do with BBC TV being in town recording a popular gardening program where they created a community park area for the locals.
Dublin was very busy, so we spent a lot of time walking by the rivers, and looking around Trinity College.
Belfast on the other hand, we loved. We took the free shuttle bus into the city, and it dropped you by the city hall. We then looked into the possibility of doing the City Hall tour, we had to pre-register & chose the 2pm tour. It was fantastic. Princess sold this precise trip for over $50, the shuttle bus was free, the tour of the hall was free - not sure how they justified the charge.
Unfortunately we have never been to Falmouth, so can't help with that one.
Holyhead was a bit chaotic. The ship had failed to get there on the previous cruise, so the town weren't prepared for two thousand passengers descending upon them. The ship ran tenders over to the quayside where a couple of small buses ferried us into town. Unfortunately for the later arrivals, the bus drivers decided to take the early arrivals on a tour of the area before dropping them off, so everyone was having to wait an hour or two for a bus. This was the main complaint of all passengers during the cruise. Hopefully they will have this all sorted out now. The town itself was very small, but laid on (un-announced on the ship) various activities & shows, along with a local produce market for us.
As I've offered to others, we live in Southampton, so if you need to know anything about the local area for before or after your cruise, please feel free to ask & we'll do our best to answer you.
Hope this helps,
Alan & Katrina