The monument / historic fort at Grand Portage has been closed each time I've been there, so I can't speak for that. However, the Grand Portage trail is pretty cool, if you're up for an 8.5 mile hike one-way (you can cut it in half by driving up Old 61). Keep going west at the end, and there's a really cool campsite right next to Partridge Falls.

If you're feeling gung-ho, you can use the Grand Portage to reach the BWCA via the Pigeon River to South Fowl Lake and North Fowl Lake (EP #70). I have not done this. When we were last there in 2006, the water in the Pigeon River was abnormally low, but probably still passable by canoe.