The standard day trip from Abbottabad is up to the Galyat hill stations — Nathiagali in particular — and back. Allow a full day with a stop for lunch. Thandiani, east of the city, makes a similar half-day outing on a less travelled road.
Naran and the Kaghan Valley — the most spectacular day's drive from Abbottabad, but really an overnight rather than a day trip. The road climbs the Kunhar River through pine forest to Naran (180 km, around five hours) and on to Saif-ul-Maluk Lake. The stretch is closed in winter.
Taxila, the Buddhist archaeological site 100 km south, can be combined with a return to Islamabad if you are not coming back to Abbottabad. The drive takes about two hours each way; the museum and the three main excavated sites make a full day.
Murree, the colonial-era hill station on the road to Islamabad, is two hours south and another reasonable day out — though many travellers find it overdeveloped.
