I wouldn't swim in the Snohomish itself, IMO -- it's deep and fast, and there are undertows. You see motor boats and fishers, but not much swimming. Anyhow, I wouldn't. I have no idea about canoeing.
You can swim in Pilchuck River, which runs along the edge of Pilchuck park on the east end of town. It's not too deep or too fast. Honestly the part that runs by Pilchuck Park I'd call a "creek" in the summer. You might be able to canoe in parts of it but I'm not sure. Never tried. There's another park farther upriver that's also right along the edge that I've never been to.
As far as I know you can also still swim in Blackman's Lake, which is north of downtown; the lake has 2 parks, and the one on the east side has a play area, picnic shelters, and I assume it still has a swimming beach. The one on the west side has fishermen and lots of ducks (we go there almost every time we're in Snohomish because DD loves ducks so much) and a smaller play area. You could definitely canoe on the lake.
A parks map: here
Snohomish also has a swimming pool, but it's closed for repairs. It's owned by the school district and with the current budget situation I don't imagine it'll be open this summer, either.
Lemme see. Oh, if you are into biking or running, or have horses, Centennial Trail
starts in Snohomish and runs north for miles and miles.