Not walkable unless you are at the town ferry terminal. If not get the hop on/off bus and harbour tour ticket. Well worth it and allows access to all city attractions by jumping on/off the buses/boats. Unlike UK, all museums attract a charge. For a day trip you can see it all yourself by this method and by walking around. Visit the old town in the centre - very quaint, if a little expensive.
Get off the ship and walk into the old town. That's your day taken care of. What a great place to see. Cobbled, narrow streets full of individual shops, cafes, bars, museums. Great viewpoint on top, but mainly flat walking. Don't go on a trip and miss this.
You need an expensive visa to do this alone, so i would recommend trips. Distance between attractions is fairly long if you walk it and you lose the commentary of what we found to be very knowledgeable tour guides. The palaces are always busy, especially the Hermitage, but you have got to see the heritage, it's stunning, as it is in the three or four other palaces available to see (St Catherines, Yusopov for example). Also combine with a river/canal cruise. Russia has come a long way in 20 years.
We were there for three days and didn't see nearly enough, so I would suggest a cruise that docks there for at least this period of time.
Gateway to Rostock, which you can access by train from right outside the terminal. Cost about Â£1 each way, or Â£7 each way if you take the ferry. Rostock has some heritage and shopping, but is a little expensive. When you come back go around Warnemunde itself. It's quaint and a little like our seaside towns as frequented in the summer. The trip to Berlin is 3 hours, so I would recommend doing the local scene. Enough to see and cheaper.
We actually docked 20 minutes away at Gydania and took a trip in.Ggansk has been completely rebuilt after the war using old pictures. Good for a morning's visit to the shops, attractions and amber stores. Pleasant if unspectacular city.