I live in East Anglia and I'm happy to endorse MM's suggestion of the North Norfolk coast. (Also check out here Southwold in Suffolk - it's delightful)
However I'll also suggest Kent's wonderful gem, Whitstable, as well. It's very flat, with some excellent restaurants, lots of independent shops, a good range of pubs and just about everything else you could want from a ('classy but not posh') seaside resort.
Copeland House offers 4 star B&B accommodation (as good, if not better, than many top hotels). I loved staying there:
http://www.copelandhouse.co.uk/
Whitstable is also a great base for exploring. It actually falls within the Canterbury City Council district, with that fine city just a few miles away. It's also on a rail line with a good service to lovely towns such as Broadstairs and Ramsgate (which has moved itself very 'up market' in recent years), so that you could explore the local pubs without taking your car:
http://www.canterbury.co.uk/canterbury-district/Whitstable.aspx