Due to weather that is getting hotter day by day, I think start of June is a good season to visit Naran and your civic can easily reach till Naran valley without any issues. The road is far better in condition than last years' and a full carpt road takes you till Naran valley. There are a few small bad patches on road that are being repaired rapidly. So road condition is not a problem.
Regarding palces to visit, I must say you should visit Shogran (your can can easily reach there on your car), stay there for a while then hire a jeep from there and go uphill to Siri and Paye, this place is a treat to watch. Then you cna stay at Pine Park hotel -Khanniyan (a river side hotel on the edge of Kunhar view that comes on-route on Kaghan) if you want to. But the most attarctive spot in Kaghan valeey is Naran where you can find more gathering around and some good hotels. There comes no electricity after the earthquake and kost of the hotel owners run generators from sun-set till 12:00 in the night. So you better keep a good torch with you. The route to Lake-Saiful Maluk starts from Naran but it is a jeepable road so you can park your car in the hotel and hire a jeep to go to Lake.
Plead read this blog post for any further information about your trip to Naran. It will answer you most of your questions.
