There are lots of places to stay, most with 10 to 15 minutes' walk of the station. Hotels are typically booked well ahead Monday to Friday by Stockholm commuters. Prices drop on weekends.
Head along pedestrianised Drottninggatan, the main street up from the station, to find the central square, Stortorget, and plenty of places to eat. Alternatively, head south of the river on Kungsgatan.
Drinking & Nightlife
Gävle is a lively student town. There are bars around the square, Stortorget, and south of the river on Kungsgatan.
If it's cold out and you're wondering where everyone has disappeared to, head into Gallerian Nian (http://galleriannian.se), the indoor shopping mall on the western side of Stortorget.