Mobility Issues in Croatia?

Getting down to Plitvice into the park requires walking down a fairly steep hill on an incline or steps or both. I am not aware of how someone with mobility issues would get down/up. Maybe - but I don't think the park operates shuttles. There are "trains" (trams) running near the top of the hill connections a few spots but they don't go down the hill. You might try contacting the park via their official website and see what they suggest.

An alternative park that is really nice is Krka National Park (north of Split), which is a lovely park too though I still prefer Plitvice. The main attraction at Krka is a huge, impressive cascading waterfall called Skradinski Buk, which dwarfs any waterfall at Plitvice. You can park your car at the town of Skradin and take a passenger boat up the river to the falls. Many people walk up along the side of the falls and explore, take boardwalks across the river at the top and cross back down the other side - but your father need not walk very far if he can't. People also swim below the falls, something you aren't allowed to do at Plitvice. The water might still be warm enough to swim in October - who knows? (In May when I was there, there were few people swimming - still very cold!)

The city of Dubrovnik is built into the side of the hill. Some of the narrow "streets" inside the old town are literally steps up about 30 degrees - wouldn't be fun to climb. If you book lodgings in the old town, make sure you understand how many steps, if any, are required to get to/from the lodging. There are very few proper hotels right at the Dubrovnik old town (which is a great area to stay) but lots of apartments and "sobe" (private rooms, maybe with private bathrooms). I stayed right outside the old town's Pile Gate, which required very few steps.

I'm pretty doubtful about Plitvice. It is a national park, not a city. The walking is not totally level. Much of it is on boardwalks with no side railings, with occasional single steps up or down. Most of the rest is on somewhat uneven ground (unpaved paths).

If your father uses a wheelchair, he will have no problem with Plitvice. All paths are paved. There are some parts which are wooden, but which would be easy to traverse. Many have no railings, however, over water.

For Dubrovnik, you will need to select your accommodations carefully. Any private residences are likely to be on the hills above the city. We stayed there, and it was 468 steps from our house to the main square. Even within Dubrovnik, there are multiple stairs on the side of the town away from water. It is flat and paved from the main street to the water. Walking the walls will be difficult.

My knees are not great. I had no problem with Dubrovnik. Can he go up and down at all? Or just a little annoyance?

Dubrovnik will be good during this time. It will be less crowded. Our rooms were charming, and half the in-season price. We were there in Nov 2014. It was cool but not cold.

All the Plitvice paths are definitely not paved. I may be mis-remembering the prevalence of bare ground, but I know it was there, because I was hobbling along on a recently-injured, untrustworthy ankle and had to be very careful at times.

The over-water walkways are, obviously, man-made. The wood is sometimes complete flat (though usually without railings), but there are some shallow steps. I can't imagine using a wheelchair. I don't remember seeing one, despite the huge number of people with whom I shared the park two years ago. It's possible that one could put together a route that would be limited to boardwalk, but I'm not sure the park map would provide the information necessary to figure it out. They sell the map in the little shop near the ticket booth. I think it cost about the equivalent of $3 or $4 when I was there.