As everyone has mentioned, you'll probably be fine on either 95 or 295 at 11:00 am on Friday. When traffic delays are less likely to be an issue (there's a BIG difference between 2 lanes in each direction and 4 or more lanes in each direction), I tend to prefer the B-W Parkway because it is a more direct shot into downtown DC and because, especially at this time of the year, it's a lot more scenic. It's a bit early for major leaf-peeping, but you'll probably see a few trees on which the leaves have started to change. It's been really dry here, though, so the colors might not be as sharp as in years past.

As to your other question, there doesn't seem to be a lot of inexpensive weekday parking in the inner harbor area. Your best bet may be to look for a garage offering a (slightly discounted) early bird rate, then walk around the area until the Aquarium opens (definitely worth a visit, by the way).