The town centre and Waterfront are both compact and easily walkable. From the train station to Christchurch Mansion is about 20 minutes on foot; to the Waterfront about 15 minutes.
Local buses connect the centre to the suburbs and outer areas, but within the historic core you will not need them. Taxis are available outside the station.
Ipswich is reasonably bike-friendly with some dedicated cycle routes, particularly along the Waterfront. Cycling to Sutton Hoo is possible via the River Orwell path for the more adventurous.