I'm not sure exactly how limited your group's walking ability will be, so please excuse any information I've provided that isn't helpful.
If you can be on your feet for several hours, walking through a park (mostly on wooden boardwalks but occasionally on a bare-ground path that is not totally smooth), my #1 recommendation would be Plitvice Lakes National Park in Croatia. It does require a night spent in or near the park, because you want to see the park outside of day-tripping hours, when it is slammed by thousands of other visitors. The conditions at such times are stressful for those with any sort of mobility issue. (I know this because I was dealing with a sprained ankle on my last visit, and I day-tripped in. Never again.) There is no danger here (beyond the potential for something like a broken wrist, I guess); the walkways are rarely more than 18 inches above the water, and the water is extremely shallow. But most of the boardwalks have no railings, so especially when it's crowded, it's hard not to think that you might end up going for an unwanted swim--not that I've ever seen anyone fall in.
I like Zagreb a lot, but the historic district is bi-level, and it's a steep walk up. Be sure you check on the availability of buses and have a map with the funicular location marked. The latter may not be of great value since I believe there are quite a few stairs to be negotiated at the top.
While staying in Ljubljana you can easily visit Lake Bled and/or Lake Bohinj. Lake Bled is what you see on practically every Slovenian travel poster ever printed. There is a good bit of bus service to Lake Bled, somewhat less to Lake Bohinj. I walked all the way around Lake Bled; naturally, the path around the lake is pretty much flat. I don't remember how long that took but it wasn't terribly long, and there were one or two places along the way to buy ice cream or a cold drink. The internet tells me the distance around Lake Bled is under 4 miles. You can also go there and just take one of the little boats out to the church in the middle of the lake. Lake Bohinj is larger, so that would be more a place just to go see.
I enjoyed the walk through Vintgar Gorge, which also can be reached by bus from Ljubljana. The walkway is not difficult at all (no scrambling over loose rock or anything like that), but I don't remember how flat it was, and it was very busy when I was there (June 2015). If your parents cannot walk at a normal pace, that might be an issue, because the walkways are narrow and don't really provide many opportunities to pass folks walking in the same direction.
There are two interesting cave systems accessible from Ljubljana. The Skocjan Caves are a bit more natural (no colored lights), but I think there's a bit more walking involved, first to get from the office to the cave entrance, and then within the caves. The Postojna Caves are more commercialized. I don't remember as much walking there (and I was accompanied by my 60-something mother with breathing difficulties), but that visit was so long ago that I can't totally trust my memory. This would be something to check with someone who has more recent experience. Definitely either cave system is worth seeing.
I was last in Slovenia in 2015, so I don't have current information on prices, but at that time I found taxis quite reasonable, given that Slovenia wasn't exactly dirt-cheap as far as hotels and restaurants were concerned. With three of you traveling together, I think using taxis to get to outside-the-city beauty spots might be quite affordable. Sometimes bus schedules are too limiting even though distances are short.
There might be a one-day bus tour from Ljubljana that would go to/through the Soca Valley. I haven't been there myself.
I found the folks in the Ljubljana Tourist Office exceptionally helpful during my visit. You could stop in there on Day 1 and see what they might suggest for outside-the-city jaunts.
