There is a popular jetty at the end of Punggol Road with ferries to the Outward Bound School of Pulau Ubin island which is just across the channel. Many locals come here to do fishing during the weekends and the atmosphere is very nice for a getaway. To get here, you can take bus no. 82 from the city area.
Update: My wife and I went to the jetty area again in January 2009. Photos of this trip are at the travelogue section of this VT page.
Punggol and Sengkang used to be farming areas in Singapore, but now there is a big housing estate there with lots of residential flats, shopping centres etc. If you want to visit this area, you can take the MRT sub-way system northeast line all the way to Sengkang station. There are LRT sub-way lines which conveniently connect you to the various locations.
The Punggol Marina located near the end of the Punggol Road is a prominent landmark in this area offers local members a place to store their boats, sails, yachtes etc. There is a nice beach located next to the marina as well as a big plot of grassland to do some simple walking.
There is a small Chinese temple by the Serangoon River located near block 116C along Rivervale Drive.
This church is one of the landmark in Sengkang and is located near to the Punggol Park along Hougang Avenue 8.
There is a beautiful park at Punggol with a nice lake, jogging tracks, gardens etc which is worth a visit, especially during evening. Many local people around the area come here to relax.
Near the end of Punggol Road leading to the Straits of Johor, there is a Punggol Marina where the surrounding areas are very relaxing, breezy and some local people like to drive there to the beach.