Have a look at my Post 1 in this thread for a starter list of 'must sees' .
PennyW has given you some good recommendations for eateries. If you want light lunches or tea/coffee and cakes try Zugers on St John's Street or Patisserie Valerie on Bridge Street or Mad Hatters on Bridge Street Row or Sally's Secret Garden also on Bridge Street. For historic or quirky settings try the crypt cafe at Debenhams (13th century Rows cellar) Oddfellows and their Alice in Wonderland upside down room or even the cathedral refectory (monk's medieval dining room though the food offering in there is not as good of late). Or try Duttons, tucked away in medieval Godstall Lane that runs between Eastgate Row and the cathedral.......So much choice.
As for accommodation,Chester has it all ....from the 5 star Grosvenor through all manner of chain and private hotels to B&Bs, which also range from distinguished to budget. The OP has a good choice for location with the Recorder's House. The nearby Edgar's House is also well worth considering as is the Manderley (if you can get a vacancy) out in Queen's Park across the river.
Do post again or send a PM if you need more specific information- and youj have made a great choice with Chester, You will not be disappointed
Edited: 10:05 am, January 24, 2014