Bonjour from Chitral,
The best mode of journey is to take a Islamabad-Chitral flight, 45 minutes but that is subject to weather.
Overland trip from Islamabad/Chitral requires a NOC from home department, Peshawar, usually takes 5 to 7 days, better to arrange it before your arrival in Pakistan, in case of flight cancellation, that'd the only option.
Agree with uselessbaba about the unfriendly behavior of Police officials at Chitral.
Birir and Rumbur, both are the best destinations but Bamborate valley is populous and touristy.
Avoid Hot spring valley, not very enjoyable because that'd been turned into a market now but do visit Chitral Gol national park and the palace, 2 hrs drive from Chitral town.
Bon voyage,