We are visiting our son in Budapest for 5 days in early April, then have 3.5 days that we want to spend in seeing Dubrovnik up through Split or vice versa... We know the weather will be iffy but should we rent a car and meander up/or down between the 2 places? Go to any island? Any thoughts would be great!
Are flights booked?
I would choose one or the other, but they are four hours apart so you could conceivably visit both.
Will you fly home from Dubrovnik or from Split? Do you have 4 nights? Are you flying from Budapest to Split or Dubrovnik?
You don't have a lot of time, and the ferries won't be running frequently in early April, so you need to take that into consideration regarding visiting an island.
You could spend all 4 nights in Split, which is a beautiful city and very interesting. If you visit Split, I recommend a private guided tour with Maja Benzon, recommended by Rick. We loved our tour with her; she is warm, friendly, and extremely knowledgeable. You can take several day trips from Split, such as to Trogir for 3/4 of a day. If the ferry schedule works out, you could take the catamaran or ferry to Hvar Town for a day. Other day trips are Krka National Park and/or Sibenik.
You could spend 2 nights in Split and 2 nights in Dubrovnik. It's about a 3-4 hour drive between the 2 cities.
Or have a relaxing vacation and spend 4 nights in Dubrovnik, to include a daytrip around the Bay of Kotor. In Dubrovnik, we walked the walls, visited the War Photo Limited exhibit, the Franciscan Monastery, and took the cable car to the top of Mt. Srd for views and drinks. Some people take a day trip to Mostar, but that would be a long day. I would rather stay overnight in Mostar, but that is up to you.
You can spent one day in Dubrovnik, visit Lokrum, and nearby Trsteno. Idea to rent a car is interesting. There are many small beautiful towns between Dubrovnik and Split and the drive is very scenic. Maybe the best place is Makarska. Its riviera is famous. Split is not so interesting to spend more than a day.