Need advise on where to start and fill 2 days

Zagreb would give you a different flavor from the coast. If you wanted to stop at Plitvice, I'd try to stay at least a night so you can enjoy the park late afternoon and then the next morning. I visited many years ago so I don't know what the crowds are like now.
Split has plenty to offer as well (have not been to Krka but bonus is you can swim there). You can take day trips to Trogir, Sibenik. I don't think you can really go wrong, but two days is awfully tight. If you do not have flexibility, I'd just go enjoy Split.

Thanks, I do have some flexibility. Do you know if there is good public transportation to the park from Zagreb? And can we get from Plitvice to Split without a car in reasonable time and cost?

Yes the bus will take you right there, then bus to Split. There has always been this story that sometimes the bus gets full and does not stop, but there would likely be another bus later in the day--I just don't how true that is, but July is high season.
Driving is much more expensive of course, but that may be worth it for the peace of mind. And then you could stay farther from the park. There are several hotels right in the park, and they are fine--they do allow you to stroll right in in the morning.

Search bus schedule here: https://www.akz.hr/
for "Plitvička Jezera"
I would inquire at the park office for the onward bus schedule when you arrive.

Thanks. That is very helpful!

good luck--I am jealous of the bike tour. There is nothing like the Dalmatian coast!