Sony's PlayStation TV, which originally launched in the US for $100, is currently available for just $20 from the official Sony Store.
While the system has been given away for free in the past (including as a freebie alongside the PS4), this might very well be as cheap as it's been on its own. The Sony Store also has a bundle that includes the system, a DualShock 3, an 8 GB memory card, and a copy of The Lego Movie Videogame for $40 (down from the usual price of $140).
The PS TV is a versatile device; in addition to playing Vita games, it can be used to play digital PS1 and PSP games, as well as PlayStation 4 remote play and PlayStation Now.
The downside is that it includes just 1 GB of internal storage, and this can only be expanded through the use of the same memory cards that the Vita uses. These have remained prohibitively expensive ever since the Vita launched; while prices can fluctuate a fair amount, a 16 GB card is currently $40 on Amazon, while a 32 GB card goes for $73.
Still, the system has routinely gone for $40 as of late, so if you're in the market for one, this might very well as cheap as you're ever likely to get it.
An interesting read via GameSpot