I assume this will be your very first visit to the Galiyaat region. Your idea of spending one month in Galiyaat is not something alien. Lots of people have homes in galiyaat and majority of them spend long vacations but usually away from Murree. Hot spots are Khaira Gali, Khanas Pur and Nathia Gali (for long vacations).
You can divide your trip in 2 parts.
First week, stay in Murree and visit following:
- Murree town itself
- Kashmir Point
- Pindi Point
- Patriata
- Bhurban
- Kohala Picnic Point
Then follow @conflicted's advice and move on to Khanapur and find a small hut on rent there. I have spent 1 week in Khanaspur and there are lots of personal houses / huts there which are available for rent. Now from this point, it will be easy for you to cover upper areas of Galiyaat region.
Visit following:
- Ayubia
- Nathia Gali
- Dunga Gali
- Mukshpuri Trek
- Dunga Gali - Ayubia Trek
- Ayubia - Khaira Gali Trek
- Namli Maira villages below Nathia Gali
- Harnoi picnic point
- Abbottabad
- Thandiani
You should be able to get a good deal on personal house / hut in Khanaspur which will suit your budget. If that doesn't work then try to find a personal house / hut in Khaira Gali residential area which is above the main bazaar. There, again u will find many personal homes / huts which are available for rent.
I would suggest to keep your personal car with you as fuel expense will be very less per day. Otherwise renting a vehicle for 1 month will cost a lot.