Tofino has many beautiful (public) beaches! Cox Beach, Chesterman Beach and MacKenzie beach are easily accessible and only a five-ten minute drive from town. Tonquin Beach is located in downtown Tofino and connects to a new 1.7km trail (the Lighthouse Trail) that weaves through the rainforest with some pretty spectacular lookout points.
In the Pacific Rim National Park Reserve, there is Long Beach, Combers Beach, Wickanninish Beach, South Beach and Florencia Beach (lots of options!)
As mentioned in the other replies, the National Park offers many short walking/hiking trails. Anything under the dense rainforest canopy will definitely keep you drier. The visitor centre close to Tofino has maps and up-to-date Parks Canada information.
There is also a museum on Wickaninnish Beach called the Kwisitis Visitor Centre, run by Parks Canada. I do believe they are open Fri-Sun, 11am-3pm.
I know Tourism Tofino’s website has lots of information on the area and activities to do in the rain and whatnot. (www.tourismtofino.com).
One thing I definitely would recommend before going out for any walk on the beach is to look at a tide guide (http://www.tofino-bc.com/tides/print.php) because there might not be a lot of beach to walk on during a high tide...
Have a wonderful trip!