When I'm in the city centre I spend a lot of time and money at Athena Games [9 St Gregorys Alley] where I get my board, card and roleplaying game fix. There's a nice community of game players based there.
If you could mention independent and small stores rather than chain stores then that's great. I'd be here all day if I named every crafting supplies stall in the market place, but it's a great place to wander the narrow alleys and look for bargains. There are fabric stalls, places to buy sewing notions, a very handy stall that will sell you upholstery foam in a variety of sizes and thickness, and even a place that sells and alters bellydancing costumes!
Heading out of the city centre along Magdalen Street you can find Anglian Fashion Fabrics [40 Magdalen St], a family run business split into two shops. One based around curtains and upholstery, and one for clothing fabrics and haberdashery. Lots of great fabrics for a variety of budgets.
For jewellery making I got to Raphael Crafts [47 St Benedicts St] who sell tons of beads and charms both in packs and individually. I love grabbing one of their bowls and handpicking out exactly how many I need for a project!
If you're looking to sell your crafty bits two places to investigate are Saint Gregory's Centre for the Arts , and Saint Andrews Hall [Saint Andrews Hall Plain]. Both are housed in medieval churches and play host to a variety of events including craft fairs.
The Forum [Bethel St, Millennium Plain] also tends to have events where you can rent a table for the day, but these are usually aimed at a specific audience, so do your research first!
If you fancy a cup of tea and a delicious cake you could also try Harriets Cafe Tearooms [38 London St] with it's retro-uniformed waitresses, or Biddy's Tea Room [15 Lower Goat Ln] for a more cosy and vintage time.
The Belgian Monk [7 Pottergate] is best known for it's collection of hand-picked vegan-friendly beers, but I go there for the filter coffee and wild boar sausage and mash!
Norwich is home to a ton of green spaces from the tiny but beautiful Plantation Garden [2 Earlham Rd] to the much larger Eaton Park with it's beautiful rotunda and pavilion, and (model) boat pond.
You can also see variety of natural places by following the walk along the River Wensum, including the Cow Tower, an artillery tower from the 1300s that's still mostly standing.
Norwich is home to a Roller Derby team called the The Norfolk Brawds who play at home at the Sports Park [University of East Anglia]. Definitely worth seeing in action!
Although the factory and shop are gone, you should still keep an eye out for Colman's Mustard [15 The Royal Arcade] memorabilia in the city. Or maybe just a pot of the mustard itself.
Museums, shops, areas, architecture etc and speaking of historical architecture, right in the middle of the city is Norwich Castle. Built after the Norman invasion it now hosts the city's most well known museum, and sits atop a hill in pleasant public gardens which also provides the roof of Castle Mall.
For a bit more culture Cinema City, The Playhouse, and Norwich Arts Centre will meet your needs for world cinema and arthouse films, comedy and stage shows, and live music and more esoteric stage performances. And a little further out of town is the puppet theatre home of the touring Norwich Puppet Theatre Company
I also like to pass the time at The Forum, a purpose-built public space. As well as holding the city's library, there's the local BBC radio station, a handful of cafes, and a large space that's nearly always home to some sort of exhibition or display. It's also the heart of the city's Pride celebrations each
Visitors to Norwich who enjoy historic views (or Harry Potter's Diagon Alley) should make a beeline to Elm Hill, a narrow cobble street lined with Tudor houses, many of which are fascinating little independent shops.
There are also two cathedrals. The larger and more well known one is home several historic buildings and gates, a Japanese garden, a labyrinth, and the grave of, and a memorial to, Edith Cavell.
Finally a walk along the river Wensum will allow you to discover a variety of great views and some surprises like seemingly random art installations!