Doors Open Toronto is indeed on today. The provincial capital is recovering from the Raptors' winning the E Conf championship last night. Street parties, hangovers and revelry.
If I was you, I suggest you buy a TTC day pass for $13 (good for two adults and four teenagers). For Niagara Falls tomorrow, make it a day trip - in, out, 5 hours? Recommend driving the Niagara Parkway from the Falls to Niagara on the Lake.
There is plenty to do in Ottawa w/o DOH - tours of the Senate, the House of Commons (both in new temporary digs) and the new Ottawa Art Gallery. PM me if want more ideas. The Grand Prix hits Montreal on June 7-9 but there will be lots of preparation underway. Don't miss Mount Royal. Quebec City is a must. Stay two nights if possible. The food is that good!
That brings me to the drive. You don't need/want to take the 401. In fact, its not even the shortest route from Toronto to Ottawa. Take 401 to Belleville, 37 to Tweed and 7 to Ottawa. Faster & more scenic. There are similar scenic routes from Ottawa to Montreal. For Quebec C ity, I would take the train.