We're arriving at 1:30 pm in Zagreb after a very long series of flights. We will spend the night in Zagreb and then rent a car the next day. Is it best to rent at the airport? We will return the car in Split. Is it easiest to return it at the airport and then take transportation into town? We're a bit concerned about driving in congested areas, especially when we'll have jet lag.
You shouldn't be doing any driving whilst jetlagged, built up areas or not! It sounds like you need an extra day in Zagreb - there is plenty to explore.
Hire a car wherever is the most convenient for you and likewise in Split. Split city centre isn't that busy or difficult to drive around compared to most towns in England and the drivers are not maniacs there, as they will let you out It is usually more expensive to hire a car from an airport than the city centre.
After a night you should be okay (I would never drive on arrival day). Of course it depends on what company you want, but a lot of them are located near the train station. I don't think it would be a difficult drive out of town from there. It's also not a terribly long cab or bus ride back to the airport to pick up there (maybe 20 minutes if memory serves). I'd worry more about the Split drop off, and would probably choose the airport drop off there.
However, if you are not planning on stopping anywhere between Zagreb and Split, there is no need for a car. The buses are really quite convenient and comfortable. That was you skip all the rigamarole and can go practically door to door!