As a Realtor/Birddog, I constantly find that Zillow is not accurate in my market. The accessed value is not the market value and that is a very important difference.
Before I became a Realtor, I buddied up with them (Realtors) and got the info I needed. If there is a listing agent in the area, you can call and ask them what other houses like their listing have sold for in the area on a similar property and see what they send you on the house they are selling. Don't ask for market comps or anything that sounds too "investory."
Some agents will do it and some won't, but it's a good way to find out the info you need and it only takes the agent 5 minutes to do it.
Most importantly, as long as you make it worth an agents time, they should be willing to help you out when you need quick things. To make sure, take them out to lunch or send them a listing or a buyer or something like that and they will want to help you as a result. I've even sent out gift cards to say thanks!
I hope that helps!