Aletsch Glacier - Best short hike?

cheapest option:
start at Moerel (between Brig and Fiesch), take first the cableway to Riederalp West and then another one to Hohfluh. You may also walk from Riederalp West to Riedrfurka.
You can't see the Aletschgletscher from Bettmeralp, but from Bettmergrat (cableway from Bettmeralp or hike).
Eggishorn is fine.
It's possible to go the the Glacier board from Riederfurka, from Hohfluh and from Fiescheralp (not Falfleralp) via Marjelensee.

Thanks Neckervd!
Your updates are always the best.
I forgot to mention that because we have the Bernese Oberland regional pass, we get 50% off on the eggishorn glacier. This 50% off does not count on any of the other cableways.
so Fiesch-Eggishorn return is 21.50/PP for us.

So how is the eggishorn view? Is the view near the end of glacier at hohfluh much better?

Eggishorn peak (2927m) is the best. If you want to go down to the glacier, take the Fiescheralp trail beginning at the cablecar station (2893m) for the first 600m, then (at 2745m) turn left (signmarked) to the steep (!) trail to point 2625m and via Taelligrat to Restaurant Gletscherstube. Go then down tho the glacier (1km). Signmarked up to Marjelensee, then you must improvise a bit.
Gletscherstube - Fiescheralp: 4 km via tunnel, 6 km via ruins of the former Hotel Jungfrau.
If you want to hike a bit more, go from Marjelensee above the glacier up to Hohbalm, then to Fiescheralp (about 12 km from Marjelensee).

Fares with regional pass Bernese Oberland:
Fiesch - Eggishorn: OW 15.40 CHF, RT 21.40 CHF, up to Eggishorn and back from Fiescheralp 19.20 CHF
Moerel - Riederalp (standard fare): OW 9 CHF, RT 18 CHF
Moerel - Hohfluh (standard fare): OW 19 CHF, RT 34 CHF

Webcam Eggishorn: http://www.swisswebcams.ch/webcam/1292513086-Fiesch-Eggishorn-%283984-Fiesch%29_Wetter
Webcam Bettmerhorn: http://www.swisswebcams.ch/webcam/1010993718-Bettmeralp-Bettmerhorn-%283991-Bettmeralp%29_Wetter

This panorama map may help visualizing the choices. http://www.bettmeralp.ch/pdf/sommerpanorama_aletscharena.pdf

Note: Not all trails are marked on the panorama map. This map shows all trails I believe. http://activityworkshop.net/hiking/switzerland/map.php?trackId=aletsch_gletscher

For really all trails: http://map.geo.admin.ch/?lang=en
click into the (enlarged) map until you get a scale of about 1:10.000

Thanks for your tips
http://map.geo.admin.ch/?Y=650211&X=142504&zoom=6&bgLayer=ch.swisstopo.pixelkarte-farbe

I think we will take eggishorn return ticket, and do a 2-3 hour hike to glacier and back. Is it possible? We will time it such that our first destination for the day is Eggishorn(reach fiesch by 9am), and then be back to fiesch to our car by 1-2pm and then see Saint-Leonard underground lake, and also Derborance lake before driving back to lauterbrunnen.

The hike from the map we have planned is
Eggishorn station - Roti chumma view point - Marjelesee and glacier - Gletscherstube - Eggishorn via seen vordelsee?

Plan to hike max for 2.5 hours (3kms per hour manageable for us)

I get a little umm, uncomfortable when I see someone planning to the nth degree. A few hours here and then an hour there, with very little if any wiggle room. To each his own of course but I have always found having an outline rather than a timetable leads to more spontaneous and worthwhile experiences.

For example, I was once hiking in Switzerland with my wife and stopped for lunch on a hillside with great views all around of peaks going off in waves into the distance. Not even a named spot on the map, just a bit of grassy hillside along the trail. As we sat there eating our granola bars etc. along came a shepherd and his flock of goats. One of his goats came up to me and starting nosing me, obviously attracted by the smell of food. I gave the goat a bit of a granola bar. The picture my wife took of that happening is one of my favourite travel pictures.

The shepherd laughed and ascertaining what languages we spoke told me that if I did that his whole flock would be climbing all over me for more. He moved his flock down the path a bit onto some grass and then came back and sat down beside us to eat his lunch. We spent a pleasant hour talking with him before all moving on. That hour was not in a timetable.

Too much planning is no better than too little planning in my opinion tsk1979. Leave time to smell the flowers, or feed the goat.

I don't check how you want to go down from Eggishorn to Roti Chumma (500m deeeper). But it's perfectly possible to go from Eggishorn to Marjelensee and back. If I had to do that, I would count about 3/4 hrs for Gletscherstube - Fiescheralp via tunnel and about 1 1/2 hrs for Gletscherstube - Eggishorn cableway station. It's just a matter of breath (at nearly 3000m).

Thanks neckervd and travelinstyle,
Regarding time tables, I am actually not planning it to the dot. I am just using the times as boundaries.
For example, if I know that last gondola at some place is 5pm, I would write 5pm in my timings as its the latest we can come back.
Ditto for first gondolas.
For example, when planning for Jungfrau, we are going to take the first train up.
So In my planning sheet I have said take bus before 6:42am because thats the last bus I can take if I want to catch the first train from Klein schedigg.
In reality we will catch a bus 15 minutes before that to get enough spare time.

So we have planned a 1.5 hour hike around Eggishorn, but we actually have 3-4 hours so if we just want to stand and stare, and do nothing, there is ample time for that.

Same for matterhorn. I know we will reach Tasch around 11am, and we have to be back at Tasch by 5pm. We have 6 hours, and we have put those times in my timetable(first and last point)
For those 6 hours, there is no plan, simple plain walking and roaming around.

Only thing hard planned is that we have to catch the paddle steamer at 6:33 from Thun :D
Thats the time the boat leaves, and then from spiez we have to catch our train connection to lauterburnnen, otherwise we reach our chalet late in the night(low number of connections late at night).