Getting to San Juan de la Peña may be complicated, but it is oh so worth it. I came to San Juan from the “back”, walking the Camino Catalán from Montserrat. That meant we walked up to the monastery from one side, and then had to take the path down to get to the Aragonés. The path down between the monastery and Santa Cruz does not require technical climbing skills, as some have asked, but it is very steep, rocky, and I would not try it if things are wet. The road is 8km but the path is only 4, so it is twice as steep as the road. I had bad knee pain for the rest of my camino that year, and I am virtually certain it came from that descent. IMO, it makes the walk down to El Acebo on the Francés look flat. But there is the road that cars use, of course. That is much longer but much less steep, but you will have to deal with cars.
The camino from Santa Cruz on to Santa Cilia is very nice, all off road as I remember. Very short and uncomplicated.
If I were walking the Aragonés starting at Somport and wanted to visit San Juan, I think there are several direct options. First would be just to take a rest day in Jaca and visit the monastery, either by bus or by taxi or by hitchhiking (hard to hitch there, but getting back to Jaca wouldn’t be too difficult if you speak Spanish and can ask people rather than standing on the road with your thumb out). Another would be to walk to Santa Cruz and stay there. As Annie says, the off road trail to Santa Cruz from the Camino has been in terrible shape, but there is always a chance someone will or has cleaned it up. I see a wikiloc.com trail from 2016, so maybe it is now walkable.
https://www.wikiloc.com/hiking-trails/jaca-san-juan-de-la-pena-santa-cruz-de-la-seros-12204916. That would be the least complicated of all, since it is only 14 km from Jaca to the monastery via that path. And then you could descend to spend the night in Santa Cruz or even go on to Santa Cilia. It has 700 m elevation gain, so you would have to factor that into your walking time as well.
But if you don’t want to take that path, you could walk along the road from the turnoff for cars up to Santa Cruz, stay in one of the nice looking places there, leave your pack and then walk up the 8 road km (or short camino km) to visit the monastery and then head back. The entire road route from Jaca to San Juan is 23 km, so that seems doable.
The backtracking option from Santa Cilia that martin1ws describes would require two nights in Santa Cilia if I am understanding it correctly, which makes it just as time-consuming as just walking Jaca to Santa Cruz. But I might not be understanding it.
Any way you slice it, it is a must-see place. At least the old monastery. The new monastery is now a hotel (which of course opens up another walking possibility, and I know vacajoe liked his snowed-in stay there). Great views from the lookout named “Mirador de los Pirineos” a little beyond the new monastery. But if time is a consideration, my opinion is that you can concentrate on the old monastery and forego the walk up to the new one.
Glad to see there are a few hearty souls intent on walking the Aragonés, one of the most beautiful. With the numbers so low, it needs all the help it can get!