it is $12 to valet park, then you give a tip to the guy who brings your car when you pick up ($2 is common tip amount) There is no time limit on the valet parking, unless you leave your car overnight...then they'd charge another $12
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We often use valet parking for the convenience of it...in exactly the circumstances you're talking about (going to MK, with a dinner reservation at a monorail resort.) Works like a charm, and is worth the cost to us (we would have free parking, anyway, since we stay at Disney hotels and have annual pass...both of which give free parking at the theme park lots.)
If you're eating at the hotel, you can do the 3-hour parking for free...but the problem is they usually check your name off the reservations list at the monorail resorts (to discourage people from parking there and going to the parks.) And, we have stayed at both the Contemporary and the Polynesian and watched them tow cars from the lots, so at times they actually do enforce the no-parking-ban. There have been times when we have seen them turning people away at the guard kiosk (you either had to be on the list of restaurant reservations, or a hotel guest at the Polynesian or they told you to turn around, no admittance. That was on a Saturday night, last spring, not a busy weekend.)
But if you're paying for valet parking, they don't care (the valet parking spots do not take away from people who are staying at the resort...the valet guys told us they just keep parking further away if they over-flow the valet spots.)
Your other option if you want free parking is of course to just park at the Transportation & Ticket Center, if you're checking out of a Disney hotel that morning, you'll still have a free parking card for your window. Then you take the boat or monorail to MK for the day...take monorail or boat to the Polynesian for your dinner reservation and then you can either take the monorail back to the Transportation & Ticket Center if you're really tired...or it is just a short walk (maybe 10 min) from the Polynesian to the Transportation & Ticket Center