Hi,
I haven't spent much time in Zadar myself, but here're some accomodation options:
Hotel Mediteran - I've stayed there once, it was nice and moderately priced.
Vila Hresc (a bit pricey, but I'm not sure what kind of accomodation you'd prefer)
There's also a Youth Hostel in Zadar.
Interactive map of Croatia is here.
If you stay in Zadar, I suggest you visit Paklenica National Park.
You can ask about a bus-line from Zadar to Starigrad Paklenica at Zadar Central Bus Station, it's a 30-45 min ride, and runs frequently.
There's also Kornati National Park near Zadar, and Telascica Nature Park. There're a couple of beautiful sandy coves on some of the islands of Kornati (on Lavernaka, I think, and some others).
Krka National Park is near town of Sibenik, not far away from Zadar.
As far as I know, the only (nearest) sandy beaches around Zadar are near small town of Nin. Croatia's coast is mostly rocky, sorry.
The distance Zadar-Split is around 150 kilometers, which amounts to around 2 hours of driving. It would be possible for you to stay in Split, of course, but then the nearest sandy beaches are around Omis town, which is even more further south than Split (in relation to Zadar).
Oh, and there is a bus-line connecting Zadar airport and Zadar city.
I hope this helps a bit.
All the best,
Anamarija