Starting at the bus station, walk up to Jalan Masjid Abidin and turn right, following it past the glowing white Masjid Zainal Abidin and continue along the way.
Eventually you'll have the Istana Maziah on your left with Bukit Puteri behind it, and the river ahead, on the other side of Jalan Sultan Zainal Abidin.
Cross the road, turn left and start along the riverside following it around till you see a small shopping centre on your left with a double escalator. Take these and continue up to reach the summit of Bukit Puteri. Once you are done admiring the view, come back down to earth and continue along the river. In no time you'll reach Terepung Puteri restaurant -- a great spot to try nasi dagang.
Sated, continue in the same direction and you'll reach the central market. If durian is in season expect to see roughly 765,984 durian vendors on the pavement in front. Go on, try some.
The market itself is a typical affair, with fresh produce and a sprawling wet market on the ground floor and cloths and fabrics on the upper. If you're a keen shopper you could easily lose an hour or two in here.
If not, veer around to the right after the market and start down Jalan Kampung Cina. This is the only easily accessible historic section of Kuala Terengganu and it is lined with traditional merchant shopfronts like you'll see in Penang and Phuket. Continue on your way, go over the small bridge and then on your left you'll pass the Golden Dragon restaurant. Just after this, on your right and very easy to miss, is a tiny alley named "Turtle Alley" which has murals and placards explaining the collapse of turtle numbers in the area.
Backtrack down the alley onto Jalan Kampung Cina and continue south; it tapers off when you have the Town City Food Court on your right and the Seri Malaysia Hotel straight ahead.
Once you're here, stop for a cold drink and a snack at Town City, then continue ahead and take a right just before the Seri Malaysia Hotel. Follow this around and you'll see it doubles back running parallel with Jalan Kampung Cina. You'll notice quite quickly a lot of bird calling. If you haven't picked up on this before, Kuala Terengganu is a popular place to farm birds' nests in bricked up buildings. The bird calls are not from real birds but rather sound systems that are played to tempt more birds in. There are a few buildings along this riverside stretch used for this, though they are right across the city.
Continue on, past the islets with their neon trees until the road turns to the right and rejoins Jalan Kampung Cina near the market. Instead of heading back into the market, go straight ahead and down Jalan Kampung Daik, which will take you back to the bus station.
The whole walk can be done in as little as an hour, but if you want to slowly wander, especially along Jalan Kampung Cina, it could take up half a day.