Local buses leave from downtown and are relatively inexpensive. For travel to places outside of Puntarenas ie, Jaco, Manuel Antonio, etc there's a main bus station. Buses are usually on time and sometimes even leave early, so plan accordingly. Don't be surprised to see vendors on buses selling snacks and drinks.
Taxis are easily accessible and can be flagged down in the street, or you can call ahead to schedule a pick up.
Most locals ride bikes or walk. You can rent bikes from any of the bike shops at really good rates. Just make sure you keep your bike locked. Helmets may be hard to find though, so you might want to consider bringing your own. Remember that pedestrians do not have right of way and that you must ride your bike in the street not the sidewalk, so be careful!
