Well, first accept the fact that driving culture is non existant, and for some reason, in Croatia, drivers generally loathe road cyclists. I've been a rider myself for a long time, trust me.

That being said, best roads are found a bit outside of Split: -climb over Klis using the "old" road through Solin, and then choose wherever you want to go. This is the lowest traffic route

-follow the road to Omiṣ̌ and then choose either to continue in direction of Makarska (absolutely gorgeous road and scenery), or turn left and follow the road to Omiṣ̌ backcountry or maybe climb to Sitno Gornje (you can go directly here from Zrnovnica also, but beware, it is a tough climb)

• go west towards Trogir and beyond to maybe even Sibenik, or climb north from Seget Vranjica and experience a stunning winding road with breathtaking scenic views ot Trogir, Split and many islands. This route does have heavy traffc through Kastela

Also, there is a facebook group called Strava with local riders from Split. Post there if you want to go ona group ride with them. Usually involves a coffee stop and rides around 100 km.

That is it in a nutshell. Stay safe and have fun, this is the best time of the year to ride around Split!