Southampton is a compact city that can easily be explored on foot. However, if you prefer, there are buses and taxis available for transportation. Expect to pay £2-3 for a bus ride and £10-15 for a taxi ride within the city.
If you have more time, consider visiting the Tudor House and Garden, the Mayflower Theatre, or the Westquay Shopping Centre. For a shorter itinerary, consider skipping one of the museums. If you're visiting on a Sunday, be aware that many restaurants and shops may have reduced hours or be closed.