What to do
Go to the Living and Learning Design Centre to get an excellent overview of the history of craft in Kutch.
Visit the Pragh Mahal and Aina Mahal museums - they are next door to each other and a wonderful insight into the history of Bhuj.
Once you are done with the museums, definitely get lost in the narrow streets of the town center - there are so many bazaars and small shops (no bigger than 50 square metres) and you will definitely come home with lots of gems.
Where to Stay
If you need all the comfort that a "western" hotel has to offer, then stay at Regenta Resort Bhuj.
Another option slightly cheaper than Regenta is City The Village.
If you are up for the experience of a homestay, then I would definitely recommend Bhujwala House. The owners are lovely and will take good care of you. They even do street food tours.
Where to Eat
As a few people can attest to, it has taken me some time to let my guard down and really just enjoy eating in India. But don't make the same mistake as I did - really just indulge in it as it is a culinary feast!! Follow these three simple tips: eat hot food; use a refillable filter water bottle and wash your hands (or use hand sanitiser). I also take grapefruit seed extract and black walnut wormwood seed extract, which seems to work but who knows if that is all just mental.
If you're staying at the Bhujwala house, your food is sorted.
Prince Hotel: Stay on the main floor restaurant for the most incredible vegetarian thali. If you are craving something fancier then head to their restaurant upstairs.
Illark Hotel: Also good for veg thalis, though they have do have other options.