How far you can take your city along? I would recommend to take it till keran and park it there. Some people will suggest you to take it till Sharda while I've even seen people taking their Merhan, Alto, City and Corollas till kel.
Better to play safe as the road condition gets worse from keran onwards and it really gets worst once you cross sharda. No problem of parking anywhere in Kashmir. You may even park your car on any road side, lock it and move on nobody will touch your car. But i would recommend to park it at some hotel due to weather and land sliding issues, people are really nice there, they'll surely cooperate. I parked my corolla at keran with AJK Tourism rest house as i stayed there for one night.
For 3 day trip in kashmir i would suggest,
Day 1. Keran and upper neelum. Night stay at Keran.
Day 2. Move to Kel, visit Sharda on the way. Move to arang kel in evening and night stay at arang Kel.
Day 3. Come back to Kel and visit Taobat (its a 6hrs drive up and down). Night stay at Kel and start your journey back to muzaffarabad on day 4 morning. You may reach Mzd from Kel in 8hours.