I've never been on the water taxi here, but I could give you this link for your own research:
http://www.chicagowatertaxi.com/
For your info, the closest stop to Union Station is the Madison Street stop. Michigan Avenue is closest to both Navy Pier (still about a half mile further east), and to Pizzeria Uno (which is on Ohio Street, at Wabash Avenue, about two blocks north and two short blocks west of Michigan & the river). Beware, though, that depending on when you go there, there might be a long wait for a table. In your case, if you get there early enough (since you'll arrive in the morning), you should be okay. However, it does take about 45 minutes for the pizza to bake, so don't walk in there at 12:45 or 1:00 pm and expect to get back in time for your 2:15 pm train. Also note that there is also a Pizzeria Due one block north of Pizzeria Uno. Same restaurant, same menu, just two locations a block apart. If one is busy, try the other.
Similar pizza is available at Giordano's (which is a favorite of some folks on this forum, though I prefer Uno), which is closer to Union Station. Cross the river on Jackson Street, and head two blocks east (south side of the street, just west of the elevated tracks). Same deal, though. It takes about 45 minutes for them to make the pizza.
