Another good choice for beginning road racers is the Saint Paul Bicycle Racing Club Beginning Racer Program: http://www.spbrc.org/what-is-brp/
. They'll teach you lots of road riding skills, take you up to the track for a day, and I think it includes the entry fee to a race that their club sponsors in July (Dakota Tech criterium, on a Tuesday in July).
Another great race for beginners is the Southside Sprints, at 48th and Chicago on July 21st, if I'm not mistaken. It's also a criterium, but they offer a clinic and a beginners-only (category 5/citizen) field.
The next road race (not criterium) coming up around here is the MN Memorial Classic, info at http://www.endurancepromotions.com/?page_id=2681
. There's also an associated crit, circuit race, and time trial, if you want to try a little bit of everything all at once.
There are also some road races later in the summer... the St Croix Omnium in late June, the Birchwood race out in Hutchinson the last weekend of July (this should be really good), and a couple others the first two or three weekends of August. Info about those will be on mcf.net as it becomes available.
I can vouch for the class at the velodrome being just about the most fun I've ever had. I was completely hooked by the time I was done with it.