Murree sucks. Feels like an overcrowded city on a mountain. Too much construction has been carried out there. Hardly any natural beauty.
In my opinion, you can do the following:
1. Go to NathiaGali via passing from Murree. This way, you see Murree as well, along with Ayubia and other places that come in the way and reach NathiGali, which is a MUCH better place natural beauty wise. There, you can trek to Lalazar (short hike, 20-30 mins only). It is a nice place. And from there you can trek to Mukshpuri top, which I have never been to myself but have heard is great. Alternatively, you can trek to Miranjani top (3-4 hours), which is the highest peak in the whole area and can get some awesome views from there. All these places reside around NathiGali.
2. Naran/Kaghan trip is a whole another beast. It is a lot more farther from Murree, NathiaGali etc. Like 6-7 hours drive from there. Kaghan comes first, then Naran. Naran is the place you wanna go. There is a small town at the heart of it with hotels and whatnot, the rest is nothing but natural beauty. From there you can go the most obvious place first, Lake Saif-Ul-Malook, either by jeep ride or hike. I have done both and Hike/trek is a much better option if you are into that stuff. Along the hike are awesome views, especially a really large glacier that you have to cross. The lake is great by the way. You can also go to Lalazar (Yeah, Naran has one too), which is like 1-2 hour jeep ride away. Really nice place which opens out when you hike for a while and gives you a nice green hilly area with tall trees surrounding it and snowy mountains at the background.
Do keep in mind that this is tourist season. As majority of Pakistani school, colleges and universities in the southern regions are off during summer, people rush into these northern areas in huge amounts. Prices in the hotels will be through the roof, everything will be expensive and you'll encounter tons of crowds.
Places further north like some others members have mention are very remote, so few people go there, meaning more enjoyment and room to admire natural beauty. Those places require tons of commitment, stamina and whatnot, so be sure you can muster it all up before planning trips to places like Rakaposhi, Nanga Parbat etc.