Ipswich is an historic town, with a street plan laid out in mediaeval times, so the few hotels which are in the central area generally don't have car parks.
The only hotel which is in easy walking distance of the town centre, with its own car park, is the Novotel (but you still have to pay for car parking):
http://www.novotel.co...ch-centre/index.shtml
However the brand new Ramada Encore might be worth considering. It's close to the rail station, which is 12 minutes walk from the town centre. Although their on-site car-parking is charged at £5 per day, they'll be offering complimentary off-site car parking from 1st June:
http://www.encoreipswich.co.uk/
The Melverley Heights Guest House is also worth considering:
http://www.melverleyheights.co.uk/
That, I regret to report, is probably your lot!
Chris