The DVP does get congested at the exit from the 401, but it is still the most direct way downtown. Take the DVP all the way down and exit onto Lakeshore Blvd (left lane) instead of continuing on the Gardiner Expressway. Take a left turn onto Lakeshore Blvd eastbound and continue until Leslie. Turn right on Leslie (Canadian Tire on your right) and drive south to the entrance for TTP.
I haven't tried parking recently because I bike there, but I think there is legal parking on Leslie before the gate and also a parking lot just inside the gate (which closes around sundown, so don't linger). Someone can correct me if they have more up-to-date info about parking.