@TJ
Regaular bus service, Coaches and vans are available in Rawalpindi for Muzaffarabd all day. For Neelum valley you can get public transport from Muzaffarabad till Athmuqam, the district headquarters. To go ahead of Athmuqam till Kel, you will have to hire a jeep.
PS my information is about 5 years old. Neelum valley is just gorgeous, dont miss it. Please take your own sleeping bags because the beddings in the government rest houses were infested and we had to scratch for many days.