Budget is somewhat enough.
First look upon following options and choose one, then I will make a plan for you with Hotel names (probably contact No. aswell) with rent and nearby POI's.
1- Kalaam, Ushu forest, Mahodand Lake
2- Shogran, siri paye meadows, Naran, Lake Saif ul Malook/Lalazaar or Lulusar lake/Babusar Top
3- Kumrat Valley
4- Neelum valley, AJK.