Most all of the Inns downtown are very nice.
Walking? You can do that, or, get a pass for one of the trolleys, or take the free CAT shuttles around downtown.
If you can make it down to West Jones St. (near the Jim Williams house) is Mrs. Wilkes Boarding House (its a restaurant) WONDERFUL food in a family setting. Can't recommend it enough. The River House on River St also has find food.
You can take the free ferry across the river to the Westin. They have food there also. If you golf, there is a golf course on the island with the hotel.
Must sees...hmmmm. The Owen Thomas house, Ships of the Sea Museum, Green Meldrim house and many many others. Go to one of the tourist stations. One is under City Hall on River St., right at the Hyatt. The other is next to City Market. They have flyers and things you can get and you might find coupons and discounts there too.
Other questions, just send me a PM. I'll do what I can to help, or, dig it up for you.