It appears that I'll have a day to spare in Interlaken in mid July. I was thinking of taking the train up to Grindelwald and maybe all the way to the Jungfraujoch. As much as I like sightseeing, I'd really like to get out and walk a bit. It's not clear to me exactly what the opportunities are for hiking in that area. I know they are many, but I'm not familiar with the region, and since I'll have just under 24 hours there I'm hoping to maximize the fun. Any pointers, suggestions, or insight into how the whole train thing works (i.e., on-off privileges) would be highly appreciated.

We took the train up to Jungrujoch area, Klein scheidegg and hiked to Lauterbrunnen, from here you can take the train back to Interlaken. We ventured around the North Face trail, right outside of train station at Kl Sch. This area gave great views of Eiger and the surrounding peaks. The trail down to Lauterbrunnen was beautiful, we had a clear day, then you can eat/relax in Laut until going back to Interlaken. If you have time taking the walk around the valley floor in Laut is worth it too, waterfalls/views everywhere - especially in the back section away from Interlaken direction.
As for hiking that area is set up as paradise. Its incredibly easy to see and follow the trails. You might not even want to plan too much, your eyes will take over.
Also the trains are never full, so you can relax on tickets/times.
You almost cannot go wrong hiking in the Jungraujoch area. We also went to Grimwald, opposite side of Lauterbrunnen valley. Wouldn't rec'd with a day, you might see lots of books/people trying to sway that town.
Have fun!

Thanks, that's very helpful. So, if you buy a R/T ticket from Interlaken to Jungfraujoch, you can get on/off the train as you please?

If you really do have a full day you can get from Interlaken to Grindelwald by train, hike past the North Face through Kleine Scheidegg and on to Wengen for a late train back all in a day and on the cheap. The milage of the hike is not that bad, maybe 11 miles. If you only have part of a day you could get to Lauterbrunnen and then gondola up to Murren or Gimmelwald and hike between the two. True Swiss Alps on that jaunt!

I think you are much, much better off hiking the area rather than spending the mony on the tourist train to Jungfraujoch.

Even with just one day you have a lot of choices in this area. I'll give you a few ideas (all or part of these I've done except the via ferrata):

1)You could hike down from Kleine Scheidegg as described above. I think hiking back underneath the Eiger Nordwand would be nice, or in the direction of Wengen, but I prefer the former.
2)You could take the train up the Schynigge Platte and hike over to the Faulhorn, descending to First or Grindelwald. You'd have nice views of the Eiger, Moench and Jungfrau in addition to the lakes on either side of Interlaken far below which is a nice contrast. (First is just a little further beyond the Faulhorn above Grindelwald as well)
3)If the weather is perfect, you could take an early train to the Jungfraujoch and climb the Moench and return. You would exit the Junfraujoch trainstation and hike to the Moenchjochhuette and climb from there. (I did this a few years ago, but in September)
4)There is a shorter via ferrata at the base of the Eiger that you could try if you do the hike down from the Kleine Scheidegg in case you wanted to make it more interesting.

The other side of the Lauterbrunnen valley is nice too, but to me if you haven't been in the area, you should at least hike in front of the Eiger Nordwand.

I'm pretty sure you can get on and off the train as you please as long as you are going in the same direction, you could just confirm this at the station.

I've spent a lot of time in this area and really love it. I even got engaged in Murren on the other side of the Lauterbrunnen valley.

I hope the weather cooperates with you!

Woodie

Wow, it sounds like I have a lot of options. How long does it take to climb the Mönch R/T in good weather/conditions?

I spent the night in Grindelwald, took the first train from there (9am), ran back to the station from the Moenchjochhuette and caught the 1pm train back down. I didn't spend more time up there since this was my 4th trip to the Jungfraujoch. Conditions were excellent. Sergio has climbed it as well this way in case you'd like another perspective.