Croatia/Slovenia/Hungary

I would first play around on Google Flights and look at your multi-city options (I'm on east coast, and flying from west coast is a whole different ballgame). Do you have time to break up the trip (say, fly to London, fly out the next day, or do you intend to do it in one go, even if booked on separate flights?)?
You could rent a car for northern Croatia (best to have one for Istria) and Slovenia, do a loop, turn it in and train or bus to Budapest.

Budapest is a needless addition in my eyes. It’s not convenient in any sense, and you’re barely spending a day or two in any destination as it is. Put those days back into Croatia/Slovenia (Ljubljana is an easy call imo.)

You’re not going to find anything non-stop here, it’s just too far and the airports are smaller. Tickets will not be cheap, so look at it from the standpoint of where you would ideally fly in and out of. This would probably be into Dubrovnik and out of Ljubljana or Zagreb. When I was searching for airfare, I found the typical aggregator sites had the worst and/or most limited service available. Dealing directly with the airline, in my case United, I found a whole slough of flights available that were not even listed via the big websites. And the price was about the same. I found pretty much the ideal itinerary through them. So, check direct with airlines and punch in your destinations, don’t try to piecemeal these together yourself.

Budapest really deserves more than 2 or 3 days. I'd hold off on it until you have more time.

Montenegro is a lovely country, though small. The national parks (not accessible by public transportation) are said to be very nice; I couldn't get to them because I had no car. The issue with having a rental car for the jaunt to Montenegro is that the driver will have to keep his or her eyes on the road all the way around the magnificent Bay of Kotor. I was very happy to sit back and look out the window of a bus.

I flew home from Zagreb back in 2015 with a single stop in Europe (maybe Munich). It helps that my home airport is Washington-Dulles, which has quite a few non-stops from Europe.

Zagreb and Ljubljana are 2 to 3 hours apart by either train or bus. I think bus service may be more frequent.

I think the amount of time you have allocated for each place seems reasonable, but what's missing
is the transport schedule and timing, which can eat substantially into the time allocation you have.

Arriving in Split on Tuesday, for example, and leaving on Friday, gives you two full days, but it's 4
days on the calendar.

Seeing Plitvice as a day trip is not always recommended either, due to the # of tour buses that show
up in the middle of the morning.

I don't think there is a train from Dubrovnik to anywhere. That is, Dubrovnik has no train station. You
either fly/bus/drive in/out.

So, my input is you have to dive a bit deeper into the transportation arrangements to be sure you know
what can fit into the amount of time you have. As for best way to/from SFO, again, you have to play with
things - Google Flights can help a lot here. If you want to minimize the # of connections/hassle, then you
are most likely sticking with one airline/alliance and that helps narrow down the options to the major hub
cities for that alliance. On the other hand, if you find a bargain flying to/from Paris, for instance, then you
might want to look into the bargain airlines in Europe (there are a lot of them) to see if they can get you
between the hub and your final destination. SFO obviously points you in the United/Lufthansa direction.

Renting a car is something you may need to do to get around Croatia and Slovenia. Public transportation
is possible, but you will lose time and potentially get lost trying to find bus stations, etc. Good news is that
it's not really an issue, other than gas costing around $8 a gallon. Buses are good between major cities,
(Ljubljana-Zagreb and Split-Dubrovnik), but less so in Bled, Plitvice, Julian Alps, etc. Flixbus is reliable
and provides very reasonably priced fares between a lot of places.

Also, rental cars rented in one country and dropped off in another incur non-trivial dropoff fees. Setting
the trip up where, for example, you finish the Croatian segment in Zagreb, drop off the car, take the bus
to Ljubjiana, and rent another car there mitigates that issue. Also, there is train service between Ljubljana
and northern Croatia.

I would also recommend saving Budapest for another time.

Hello to all who responded with your suggestions...truly appreciate it! LOL, when I look at the map the countries looks so close and doable for getting to/fro. Of course the "devils in the details"...so based on your feedback we'll save Budapest for another trip. I've been using Kayak to check on flights but just now got on to Google Flight and can see that it's laid out more clearly with more options so I will pursue that angle. Yes, I will definitely spend more time dialing in on our mode of transportation & associated time allocations for getting around. Back to the drawing board and thanks again for your input! I'll likely be back with more questions :).

Good choice--you will find so much to keep you within Croatia and neighboring countries.
My first impulse would be to do the kayak trip first, with maybe just a day or a few days before. But it really depends on how the flights work out. I think mid September will be ideal weather for that part, which is the most season-dependent. And ending in Istria in October during truffle season would be really nice, if you are in to that kind of thing!

If you had saved your trip to Kotor for the last day and continued a bit further to Podgorica, there are direct flights to Budapest on Tuesday and Saturday for about $100 (90 minutes). It's how I would get home from Croatia.

Actually after seeing Dubrovnil, Kotor isn't that special, but Perast and Budva can be interesting.