Never been. But just grabbed a quick look at my Heikell. 17 anchorages are marked on the east coast. Only two on the west coast, and they are only 4 miles apart. So sailing around the island might mean a long leg around the west side. Of course Albania is only a spit away if you want a bit of adventure!
Angi on the northeast coast, just down from Kalami and Kouloura. There is a small bay at Angi and one just slightly to the right towards Kalami, this is the one where people usually drop anchor.
At Angi Taverna Nikolas (Far port side of bay) have some of the best food I've eaten in Corfu and a little jetty for your tender. I think they also do a water taxi service. You can also walk along (short stroll) to Kalami and have lunch in the "White House" where Lawrence Durrell wrote Proseros Cell. You can get provisions in Kalami although don't expect much.
Koulora just north up the coast has a little harbour that you probably wont be able to moor in but the bay is quite sheltered. It's a really beautiful hamlet with a good little restaurant just above the harbour.
Kassiopi, Corfu town and kavos would probably be best for getting provisions in.
Can't really help you any more with anchorages but can tell you where's nice and where's not if you can tell me where you're thinking of. I suspect you will have difficulty with the west coast as it is mainly beaches Globetrotter do a good Corfu guide.