I too live in Williamsburg, it is a great place to live

. Since I live here I don't really frequent the hotels but I can tell you what I've heard. Most people like the Bypass Road area as these hotels are newer and cleaner. I know nothing about the Governor's Inn so I can't help there.
Restaurants: There are a lot of chains and they're usually busy. A few more local places we like are Sal's (Italian and yummy, near Books-A-Million), Peking (GREAT asian buffet), Jimmy's (a little far but really good food!), Shackleford's (great food near Target) to name a few. Of course, no trip to Williamsburg is complete without going to Pierce's.
Seeing CW is worthwhile but I would also recommend going to Jamestown Settlement. It's a very educational and fun place.
I'd be glad to answer any more questions, just PM me!