City Suggestions
 

I am currently in the planning stages of a 78 day trip in Europe with my Boyfriend. We already have tickets Arriving in Stockholm, Sweden April 27th and leaving Dublin, Ireland July 15th 2016.
The route:
Sweden - We will be here 9 days staying with a friend for free.
Amsterdam, Netherlands - For a weekend.
Munich, Germany- For a week.
Italy- 2 weeks. We are meeting a professor I had gone to Europe with previously for the first for days of our trip in Rome. Definite:Rome, Day trip to Pompei. Possible: Florence, Sorrento, Capri (suggested by the same professor we're am meeting.)
Paris, France - For a weekend.
UK - Staying for 3 weeks to a Month. Would love to see Wales, Britain, and Scotland. I have been to Scotland before but stayed mostly in St. Andrews the entire time.
Dublin, Ireland + others. - 3 weeks.
What I'm looking for are suggestions places to see, places to stay any trip recommendations in general. We will be using Airbnb to find a majority of the places to stay during the trip.

Seems as if you're giving Amsterdam and Paris short shrift but perhaps you've been to both before? Ireland is very pretty, wonderful people, great trad music--you could do a very comprehensive tour of the Republic and Northern Ireland in three weeks, just depends on your interests.

Main touring bases for Ireland are
Dublin for mid east, Waterford or Kilkenny (or Carlow) for South east.

Cork for south west

Killarney/Kenmare for Kerry

Ennis for Clare & the former Shannon region.

Galway for middle West coast

Sligo for North Mayo to Donegal

Donegal/Letterkenny for the north west

Portrush/Portstuart for Antrim coast and Glens

Belfast for the north east

There are 4 provinces to the island of Ireland and you could easily fill a week just seeing some of each individual one, hardly comprehensive?

As answered on your other question,It is easier if you separate the Individual countries

What do you want to do in Munich for a week?
I would add at least a day to Amsterdam and probably two to Paris.
Are you allowing travel times in your planning? How are you planning on getting around? Train? Plane? Car?

In Munich make sure you take a couple of day trips to the south, easy train ride to Garmisch which should not be missed. Also nice day trip to Nuremberg. Go on the BMW tour in Munich.
Please spend time in NI. Belfast is a great city and the Antrim Coast is beautiful.
Give Paris more time or you will be sad you didn't. I would say at least a week.

I would not spend so many days in Stockholm much as I love it - but would carve out 3 days or so to see Copenhagen, which is charming and has tons to see and do.

Agree that Paris and Amsterdam are given very short shrift unless you have been to both before and this is just a catch up.

I would not spend so long in Munich but pick a town in the south near the Alps and spend several days there with a car so you can easily get around. (Assume your other travel is train and/or plane.)

Overall you are doing just cities in many areas and I would allow time for some other day trips to get more of a flavor for each of the countries.

And while 3 weeks isn;t bad for Ireland it really isn;t much the England, Scotland and Wales - since IMHO you really need at least 5 days (6 nights) just for London) - which is huge compared to any of the other cities.