HI caitm -
Welcome to MySwissAlps.
<<"However, the area with Murren & Lauterbrunen & Grindelwald & the hikes there look great and if its feasible I'd like to fit that in too.">>
<<" I don't want to be constantly on a train though, unless it is one of the ones with amazing views, or have a crazy itinerary.">>
You can split the trip into two parts...it is possible and not at all difficult. The train rides are not onerous. The timetable will help you out:
The hotels that are open in the Jungfrau Region will have plenty of rooms in mid-June. That is when things start to open up after the Spring shut down with no skiers, and maintenance of transport equipment.
The gateway to the Jungfrau region is Interlaken Ost. From there, you go into the valley and up the mountains on various kinds of relatively slow mountain transport.
The train from Luzern to Interlaken Ost runs once per hour at xx06 and takes 1 hr 49 minutes. From IO to Wengen takes 44 minutes every half hour.
As a factor to consider in making your plans, high Alpine trails such as this one:
normally open on about June 15th, with considerable variation based on the Winter snow pack. The trails need to be free of snow, but also snowslides have to be a considered as a factor when opening a trail for the hiking season. Early June is the tail end of Winter at altitude. On the Lauterbrunnen Valley floor, it is Spring.
I was up there at Männlichen above Wengen at about 2300 meters one June a couple of years ago, on the 15th or 16th, and the trail had just opened. Lots of soggy snowdrifts here and there. We did not take the hike though, because the clouds were thick. And, even though they usually come in layers, the the clouds and fog were present all the way down to Mürrren. We ended up going to Brienz.
The weather changes rapidly, but staying only one day in the area is coin-toss. Forecasts are usually reliable at most 24 hours in advance, and 12 hours still is not a promise.
Luckily, it is also possible (if tiring) to base in Luzern, take the train to, for example, Wengen or Kleine Schedegg, look around a bit, and return in one long day. The train ride is reasonably scenic. Once you get past Interlaken Ost,, on the way into the Lauterbrunnen Valley, and especially after you leave Lauterbrunnen and start to climb seriously, the trains are slow...cog-wheels trains, narrow gauge track, steep grades. You can sort out the weather the night before (webcams, weather forecasts )and check at the tourist info by track #2 in Luzern, unless you leave before they one, or at Interlaken Ost.
Many people find this site to be as accurate as is possible in a country with rapidly changing weather:
You can work that trip out using the timetable. Please read the introduction page carefully.
That is a long day
By the way, you might find this bit of light reading to be useful:
Personally, I prefer Wengen to Mürren, but there are certainly opinions on both sides of that issue. ;-)
In June, Spring is well advanced, almost into Summer near Luzern. Much lower altitude.
The nearby mountains can give you a taste of the alps.
There is a lot of hiking available around the lake, of varying difficulties. Here is one example:
Opinions vary, but I vote for the lake boat rides on Lake Lucerne to be the most beautiful in Switzerland, especially in the southernmost part. There are a few relevant pictures in that thread.
If you were two weeks later, I'd suggest basing at Wengen, or near the Jungfrau. With your dates, I'd suggest basing in Luzern. However, if the limited trails availability and general weather conditions don't trouble you, then I'd advise using two bases, and take a chance on the weather,