Northwest or Southwest

I would go north.

I'm 'struggling' which to answer! We have not 'done' the Ring of Kerry but we spent about 2 nights in Dingle and 2 in Castlemaine. We were able to catch a couple of evening concerts in Dingle, which were great. We enjoyed our time going around the Dingle peninsula (good museum on the D. peninsula with history about the Blasket Is). We also really liked visiting the Burren (maybe you will visit with your friends?) which is north of Ennis. We could've spent more time in the area, still without getting to the Ring of Kerry. We also visited Cork, briefly, but I can't remember what we did there--maybe a museum.

To the north, we also really liked our visit to Galway and driving around the Connemarra. We did not have time to walk or hike.
We LOVED our time in County Donegal, particularly going all the way to the top of 2 peninsulas---up to Fanad Head, and to Malin Head (two separate trips). We just headed out and rambled around the peninsulas, stopping at little villages along the way. We visited the castle in Donegal town, but only on our way south.

However, if you are all the way to the top, you would also want to visit Derry (see Museum of Free Derry) We visited the Monreagh Heritage Centre not too far from Derry. We lucked out by meeting a gentleman who had been involved in the Good Friday Agreement/Peace Process. He even drove us around some of the area! The Ulster Folk Museum in Omagh, a little further away, was wonderful (one of my maternal lines was Ulster Scots who had been in Northern Ireland a few generations). These should be added to a future trip!

Given that you will only have about 6 nights out of Ennis, it probably makes sense to enjoy the area closest--Cork/Kerry. Or, chose Galway, Mayo or Galway/Mayo. Or, take the train to Derry (I don't even know how long it takes; it is a long drive) rent a car, and spend your 6 days/nights in Co. Donegaly. I smile, thinking of this option, but it would still be rather rushed without a lot of time for hiking, biking, etc. My husband loves to look at real estate in Donegal and dream.

You will have a wonderful trip, whichever direction you choose. Ireland really spoke to us.

Gosh, the train from Ennis to Derry would take you between 9 and 10 hours.

I wonder if it is worth going from Ennis to Dublin Airport, flying to Donegal on the evening Aer Lingus flight, renting a car there, then driving back down to Shannon in the ensuing 6 days, returning the car at Shannon.
There are no useful flights for you to Derry Airport or I might have suggested that- although that would be a cross border rental.

A loaded question indeed. The far southwest of Ireland was one of the most delightful places I've ever been, so for me, the choice to go south (specifically southwest, not southeast) would be an easy call. But...

How many full days do you really have to work with? Be honest...don't count your arrival or departure days, don't count days you already have plans for.

Will you have a car?

Whatever you choose, you will enjoy! My personal choice would be Galway/Mayo and Donegal - They tend to be less busy and scenically as good. Slieve League Cliffs are the some of the highest in Europe. The Skye Drive is possibly the best short drive in the world on a sunny day. Go for a cruise on the only Fjord in Ireland (Killary Harbour).Drive the Lost Valley badly affected by the Irish Potaro famine and half the population died. Explore Achill Island... There's lots of history to discover too from places like Carrokeel Megalithic complex to Ceide Fields. There are ruined abbeys (Cong, Ross Erril, Donegal) castles (Aughnanure, Athenry, Glenveigh) and lots more waiting to be discovered.

The Folk Museum at Castlebar is wonderful. As well as artefacts of a lost way of life, there are many videos of people talking about life and customs in rutral Ireland in the 1950s and 60s. It is an eye opener.

We did this boat tour. The owner, Paddy Byrne, is very entertaining! We stayed here that night. The beach there was amazing!

Wow, that is a long train ride! I expected it would be pretty long. It was a long drive.

I just don't think that there is enough time to do Donegal justice because of the distance...believe that you will return!

Wonderful responses. Thank you to all who replied.
We will have a car the entire time, picking up and dropping off in Shannon.

Sounds like there is no bad choice here.

Though I want to say either is great, I'll advise you to go southwest.

You mentioned being active, liking history and eating healthy. Go to the Dingle, Kerry or Beara peninsula because each has great hiking, have a ton of history -- especially Dingle -- and draw from the waters for superb cuisine. One detail about hiking: In 2010 I walked the 100 miles of the Dingle Way trail (https://www.dingleway.com/). It was among the best things I did in travel.

Since you'll be there in June, the countryside will be glowing and even blooming.

The key element for you (I think) is your timing, ie planning your visit in mid June. At that ime of year you'll share your experience in Dingle and Kerry with tens of thousands of other visitors. Beara will be the exception - the tour buses still don't go out there so it's relatively unspoiled. Lots of great hikes too.
If you opt for the northwest you'll have large tracts of Sligo and Donegal virtually all to yourselves. Connemara too for that matter.