I haven't been to the "new" Sparks museum, but I've heard it is great. You can spend a whole day or more in Fairhaven easily - there are two nice parks, great bookstores (Village and Eclipse), a nice wine store that has tastings (Purple Smile). In the summer there are two tours - a Sin and Gin one that focuses on downtown and a ghost tour in Fairhaven.
The marina is usually a nice place to wander in the summer, but there was just a tragedy there so I haven't gone down there lately.
Whatcom Falls park is a nice meander type of place to hike. Big Rock Garden is a little hard to find, but also a nice place to spend a few hours in the heat of the day.
Lummi isn't that fun as a day trip (in my opinion) - we usually zip up to Baker for a day trip instead.
There are a few whale watching tours - I recommend the one that has the salmon dinner on the way back or the sunset tours (but that runs on Wed. I think).
I don't know much about the B&B situation - there is one within walking distance of Fairhaven that always seems full. The one on Garden street I've heard is nice but parking is a bear in that area.
Most restaurants have veggie options - what kind of food does your Dad like?
We lost a lot of our antique stores a few years ago - there are a few left and those are good, but it isn't like it used to be.
As for cars, there seems to be a car show somewhere in town almost every weekend in the summer - if you check the Take 5 (in the Thurs. Bellingham Herald) it will list the weekends that have one and where.
If your Dad likes movies and it is raining out - the Pickford is really nice and if you pick a movie playing in theatre 1 you can take beer or wine into the movie.