I have no experience staying in Winchester, but this place always looks interesting when I walk past it.
http://www.justab.co.uk/

It's 5 minutes walk from the town centre, and 5 minutes from a public car park (car parking in Winchester is always an issue.

Alternately, there is the Black Hole (http://booking.theblackholebb.co.uk/default.aspx)
The name is a bit of a joke - The owners also own the nearby Black Boy pub (recommended), and the Michelin starred Black Rat. Again close to town and parking (although 20-25 minutes walk from station.

>> arrive Heathrow in the morning, rent car, travel to hotel in Winchester, quiet day, some sightseeing, but recovering from flight from Canada
- day 2, Windsor Castle, Oxford, back to Winchester<<

I'd make one change since you will be arriving at LHR which is only about 7 miles from Windsor.

I'd (really) seriously consider staying IN Windsor that night, visit the castle that day if you aren't too jet lagged -- if not, visit the castle the next morning. Then visit Oxford if you want, after which drive down to Winchester for the next 2 or 3 nights. Then on to S'hampton.

This will save you both a drive to Winchester while jetlagged, and quite a a bit of to-ing, fro-ing to see Windsor and Oxford.

I love Winchester and concur wholeheartedly with those who recommend it. Also agree with JanisJ re: Windsor first, then Oxford, then Winchester. In Winchester, we stayed at the King Alfred (rooms over a pub) and really enjoyed it, but I've always thought the Wykeham Arms or Hotel du Vin looked lovely - and they're right in the city center. Winchester is quite compact and very walkable, so don't worry about staying a little ways from the city center if it's easier for parking. Have a great trip!

Sorry - I meant the Old Vine looks lovely. Not sure about Hotel du Vin, but I've walked by the Old Vine and thought it looked very nice.

Stayed at the Hotel du Vin some years ago. It as excellent as was their restaurant.

HdV gone bust a couple of times in the past few years.

That's interesting. All of them? I know they had several other hotels/ restaurants through out the U.K.

someone always seems to buy up the brand and keep it going.