There's a lot to see in the Aletsch Arena, and a fair bit of cable car and hiking trail infrastructure makes this possible. I only had time to do one hike, and so I encourage you to check out the Aletsch Arena website to find an activity that's right for you. You can find the panorama map here.

         I took a round trip train that ended up being about 6 hours total from Zurich to do a day hike. I initially planned to follow this guide from r/ali_on_switzerland, but it didn't quite pan out that way. However, I met someone from the Czech Republic following that guide during my hike which I thought was a cool showcasing of the impact and reach helpful travel guides have.

         I recommend going up to Eggishorn by cable car to start. There's a nice little restaurant there with good views, and if you are prone to altitude sickness at all it will give you a chance to rest a bit. Not that I think altitude sickness is really a problem on any of these hikes, but just in case.

       Walking across the rocky path up to the Eggishorn will provide one of the most impressive views of the glacier and the 4000m mountains along the horizon, and you can see the distinct shape of the Matterhorn in the distance.

        I then backtracked to the restaurant before heading to Bettmeralp. I hiked along the UNESCO Hohenweg trail instead of going down towards the glacier. This trail might be a bit nerve racking for people unused to heights, but it is safe despite the rocky appearance. I cannot remember the exact length of the hike, although I don't think the hike is that long, but I did spend a lot of time just admiring views from Eggishorn and the restaurant. Luckily the cable car at Bettmeralp down to Betten Talstation is open pretty late, and so it was possible to head back to Zurich without an additional long hike down the mountain. 

      The town of Bettmeralp itself is quite pretty making it a nice area to end any hike you may choose to do. I walked into the Bettmersee, but hopped out almost as soon as I stepped in because it was freezing cold. The freezing water temperature didn't seem to deter a little Swiss girl swimming in the middle of the lake with a pool noodle, and so it seems that if you're more adventurous than me the lake provides a nice swimming spot after a hike. 

     Always make sure to have good sun protection and water, but especially for hiking here. There's no place to get water besides the start and end of the hike, and hiking on the ridge line at high altitudes means you are heavily exposed to UV light. 

    In summary, I really enjoyed hiking in this area, and I think it is a pretty good destination to try and see. However, at least the hike I did was a bit repetitive in terms of views, although the views are really good, but if you do the hike faster you would probably have time to see a bit more along the way. I also think my feelings are a bit biased because traveling from Zurich resulted in a very long and tiring day, and this is something I note when doing a long train ride to Zermatt as well. However, if you are staying in an area closer to the glacier I would definitely recommend adding it to your itinerary.