Zen Studios has finally provided a concrete date for Zen Pinball 2 on Wii U in North America: Thursday, March 21. The free download will be available on the eShop next week, which lets you sample all available tables in Zen Pinball 2's vault for a limited amount of time before purchase is necessary.
Tables are purchased piecemeal through the in-game store, tables including the stock game tables and DLC such as the Marvel Pinball series and the Plants vs. Zombies tie-in. The freshly minted Star Wars tables have not been announced for Nintendo platforms, so naturally there's no mention of them in the announcement.
Finally, we'd be remiss if we didn't mention that purchases on other platforms won't transfer over to the Wii U. Zen Studios offered cross-play on PS Vita and PS3, but since the 3DS and Wii U use different stores, transferring already established content from the handheld to the Wii U is impossible.