What are the best sights to see in Vancouver? And hotels which are nice as well as reasonable prices. Just myself and my husband coming from Seattle with a rented car. Do we need our U.S. passports?

Yes you need your passports.
I'll give you my short list. Granville Island, Stanley Park, Canada Place and Gastown.
You will only need the rental car if you want to see things outside Vancouver. Paying for parking on a rental car makes no sense to me.
Take either the Amtrak bus or train from the newly remodeled King Street station to the Vancouver ViaRail station.

The Hotel Vancouver is a nice hotel and where I usually stay.

The best sight in Vancouver is the Beaty Biodiversity Museum.

You need your passports yes and if you or your husband has a DUI conviction you are inadmissable to Canada.

Don't miss the Museum of Anthropology on the University campus. Wonderful setting and the native display is magnificent.

I agree with Museum of Anthropology and Stanley Park and will add Lynn Canyon (Suspension Bridge) and Grouse Mountain to the list. Queen Elizabeth Park and the Van Dusen Gardens are terrific if you like gardens.

Great suggestions there for you! I would also add the Capilano Suspension Bridge <http://www.capbridge.com/> which we thoroughly enjoyed. Also, my favorite meal there was at Calabash (Caribbean) which had amazing jerk chicken, poutine and roti <http://calabashbistro.com/>. You need a reservation if you go for dinner.

I haven't been to the Beaty Biodiversity Museum - thanks for that Improvisor!