I have a few suggestions. I'm assuming you have a budget because your title is way-generic. If a media player with wifi is all you're looking for, then that can be anything from the oldest iPod touchest to the most expensive of smart phones, including all those quirky touch devices that run their own firmwares outside of Android. I'm going to go ahead and impose my own set of limitations on you so that I can narrow a list for you to choose from. These devices pretty much have the minimum hardware requirements for Android 4.0 and screens smaller than 7".
The Polaroid PMID4311, Emerson EM543, and Uniden 4.3" Tablet were part of a recent biglots promotion for $50. These are apparently not for sale anymore on their site and I can only guess they're only available on eBay. All three seem to share exact hardware specification. GBATemp user BenBK recently picked up the PMID4311 and had interesting things to say about it in the Android section. I can only guess that the other two perform the same way. PMID4311 and EM543 can now be found on eBay for $90 unused. The Uniden can't be found anywhere. All three have 4.3" screens.
The Android Pocket Rock and JXD S18 are chinese wholesale-sold devices. Their $50 pricetag and ambiguous chinese origin should be an indication of how great these things are. On one hand, they're sold in a chinese whole sale for $50, on the other hand, they're $50. Good luck finding someone selling the Pocket Rock, and the S18 is the only device on my list with a resistive touch screen. Both have 4.3" screens. Originally the Android Pocket Rock was $50 but now goes for $120 on ebay.
The Gardner GBT6 is going for the same price on eBay as the BigLots three ($90) and its the one that I bought for myself as a dedicated music player for work. Its hardware and performance is just as crappy as the devices above but it's far more aesthetically pleasing than the others. It looks and feels nicer than the others listed above. It has a 800x600 pixel 6 inch capacitive screen. Its uniqueness is also a great downfall. Finding screen protectors and cases on the cheap is impossible for a 6-inch screen. There are also no review articles or rooting/mod tutorials to be found. Having only had mine for 2 hours, I can't even tell you how compatible it is with market apps. Actually going to make a thread real soon on it.
Anyways these are your best non-cell phone budget devices that have wifi. All smaller than standard tablets. All suck. All run Android 4.0. All have 1Ghz processors with 512MB RAM and a Mali 400 GPU. All under $100. All microSD expandable and no Bluetooth.