All of the state but unfortunately you can't. So any place that doesn't have military restrictions is good in Kashmir, particularly from Srinagar onward. Once in Kashmir, make sure to visit the local tourist office that will advise you all about safe places to stay. I'd like to add that any place you go in the interior, and it becomes more beautiful exponentially, the more you go higher up or beyond Srinagar, if you can manage homestay, there is nothing like that for the people are really beautiful and lifestyle in remote areas of the valleys there is simply amazing and full of a promise of a rich local culture experience.
That question will not do justice to J&K. As you should probably be taking a month's leave to explore that place on earth. Every destination you visit in that place will hold you tight. You shall leave you part in those valleys once you come back.