We always end up catching it last minute near the bridge to Tomorrowland. We usually get there right as it is almost about to pass, and we usually get a great, close view without waiting. This is in July...but I'm sure if it works in July, It'll work anytime!!!
In February we were having a late lunch(2:30) at Pecos Bill in Frontierland and were sitting at a table outside. At 3:00 the parade started right there. We were able to sit, eat and watch.
I am an expert of this spot, it's in front of my breakroom. Everyone crowds near and underneath the Train Station but hardly anyone thinks to walk across the street to the curb facing them. So you can get there about 20 minutes before the parade and have it to yourself for the most part. It's the curb facing the train station, the hub with the flag pole and Roy O. statue. A word of caution the parade will not get there until 15 minutes after the parade actually starts.
I've always like standing on the upper level of the train station to get good pics of the floats and characters. If you want to be on the ground level and interact with the characters, the flag pole island is best!
At the fire house. It is at the end of the parade route, and nobody thinks to go stand there. The airconditioned air flows out of the shop and cools of the area in front of it. It is amazing to see that less than 15 feet away there is a crowd three people deep, and you are sitting down with space on either side of you.