Though, unless you're planning on staying in one of the local hotels, there's absolutely nothing to do here; it's the most pointless resort we've ever seen. In fact, the whole town consists of a few restaurants, a museum, a large marina and expensive villas and hotels. There are virtually no waterfronts, walking streets, or public spaces. Even if you live in a hotel, there is simply nothing outside of it.
If you still want to walk, then park for free at the only interesting place - Parrocchia Stella Maris church (41.133277, 9.530379), at a nearby parking 41.132977, 9.527008 or at the paid underground parking here 41.134564, 9.538109.
There is not much to walk around, there are literally a few pedestrian mini-zones around the bridge 41.132808, 9.536742. If you want to go further, you can do it only along the paths for boat owners.
There is a small park on the hill with playgrounds and views of the town. If you have children, you can stop by (41.139882, 9.528011)